Esteban HerndndezEsteve BANCO DE ESP ANA

COMMENTS ON SOME OBSCURE OR AMBIGUOUS POINTS OF THE TREATISE DE COMPUTIS ET SCRIPTURIS BY LUCA PACIOLI

Abstract: Recently, the author translated Luca Pacioli’s treatise De Computis et Scripturis into Spanish. During the translation, the author faced a series of points contained in the text which are not clear and which present some difficulties of interpretation.

This paper shows the main points that are confusing, what constitutes their difficulty, the interpretations given by different specialists and, finally, the interpretation given by the author himself with the reasons he had to adopt it. In this way, it is to attempt to clarify the question, to offer a basis for judgement to those who are interested in this subject and, above all, to submit the position and interpretations adopted by the author to open discussion.

Among the various doubtful and obscure points, the following ones are considered in this paper: the contradictions and ambiguities observed by some authors in regard to the treatment of the balance and closing of accounts; the discrepancies shown in several passages of the Treatise which give ground to the hypothesis that this Treatise is actually the result of the juxtaposition of two or more different texts, written at different moments and for different purposes; the particularities of two payment methods of the purchases which Pacioli distinguishes expressly (by ditta and by scritta di banco); some ambiguities regarding the way to keep the accounts with banks and official bodies; various instructions concerning the location of the accounts in the Ledger, the situation of the date, and so on, which seem paradoxical and contradictory; and other ambiguities.

*A version of this paper was presented at the 16th Annual Congress of the European Accounting Association held in Turku, Finland, April 2830, 1993. I thank very much Prof. Basil S. Yamey for his kind observations to this previous version. I also acknowledge with thanks the useful comments made by Carlo Antinori, Antonio Goxens Duch, Pierre Jouanique, Yannick Lemarchand, Antonio Lopes de Sa and Ernest Stevelinck. All of them have contributed improvements to the paper, The remaining faults and errors are entirely rny responsibility.

INTRODUCTION

When I recently translated Luca Pacioli’s treatise De Computis et Scripturis into Spanish, a series of obscurities and difficulties of interpretation were uncovered.

In this paper, I intend to discuss — though without any pretensions of exhaustiveness — the main obscurities encountered, their difficulty, the interpretation given by a number of scholars who have studied the subject and, finally, my own interpretation and the reasons that led me to consider it as the most correct. This paper is thus an attempt to clarify the questions raised, to offer a basis for judgment to those who are interested in it and, above all, to submit my approach and interpretation to open discussion.
As I point out in my introduction to the translation, Pacioli’s prose is surely neither easy nor fluent. Baldi and Annibale Caro, among old authors, and Federigo Melis, among modern ones, have already mentioned this.

The difficulties of this prose are many: it is written in a half Tuscan, half Venetian language: it is still unpolished and lacking clear and precise rules; the book itself is incunable with the typographical limitations and; above all, it is complicated by abbreviations characteristic of that time. For all these reasons, Luca Pacioli’s Treatise contains various types of anomalies, inaccuracies, ambiguities and obscurities that will be convenient to group in different categories for the purpose of this analysis.

First, there are purely typographical anomalies and irregularities or mechanical errors. We shall not lose much time on them, although I shall point out the main ones.

Second, we shall study a small group of obscurities and ambiguities which are basically of a linguistic nature and whose interpretation may cause headaches to translators, though they do not really affect the technical aspect of the work.

The third group consists of points whose doubtful interpretation does affect in one way or another the accounting, commercial or banking explanations given by the Franciscan monk of Borgo Sansepolcro. This is the largest group of difficulties, obscurities and ambiguities.

Luca Pacioli: De las cuentas y las escrituras. Tituto Noveno, Tratado XI, de su Summa de Arithmetica, Geometria, Proportioni & Proportionalita, edition y traduccidn por Esteban Hernandez Esteve, con una reproduction fotogrdfica del origina, Asociacion Espanola de Contabilidad y Administracion de Empresas (AECA), Madrid (1994).

Finally, I shall explain some details or passages that make us doubt whether the particular Treatise De Computis et Scripturis is really a single work entirely written on the same occasion and for the same purpose.

TYPOGRAPHICAL ANOMALIES

In this section, I shall mention three irregularities and one anomaly or curiosity of little importance.

The first one appears in Chapter 11. When mentioning the terms and expressions which introduce and identify the debit and credit accounts in the Journal entries, Pacioli says that they are Per and A, i.e., From or Debit and To or Credit, respectively: “Of which, the first one, From, is always written at the beginning of each entry because the debtor must be specified in the first place and the creditor immediately after, separated by two lines, in this way:”.2 The text next shows two parallel vertical lines. However, in the examples of Journal entries provided throughout the Treatise, Pacioli or his printer do not use two lines as a separation mark between the debit and credit accounts, the latter being introduced by the preposition To, but simply use a full stop or a colon. This typographical anomaly has already been extensively discussed by Basil S. Yamey in 1974, specifying that, at that time, the expression virgolette meant two slanting lines.

The original sentence, maintaining Pacioli’s spelling but completing the abbreviations and using the current punctuation rules, as I shall do in all the quotations from Pacioli’s text, is: “Deli quali, sempre nel principio de ciascuna partita si mette el Per, pero die prima si deve. specificare el debitore, e di poi immediate el suo creditore, diviso lun dalaltro per doi virgolette cosi:

Basil S. Yamey: “Two Typographical Ambiguities in Pacioli’s ‘Summa’ and the Difficulties of its Translators”, originally appeared in GutenbergJahrbuch, Mainz, 1974, and reprinted later in Basil S. Yamey: Essays on the History of Accounting, New York (1978). In his wellknown work La Ragioneria, Fabio Besta mentioned this anomaly and pointed out that the correct translation of virgolette was “lines”, though without specifying whether vertical or slanting:

L’uso largo delle due virgolette, nell’antica loro forma di due lineette, tra i due titoli dei conti richiamati in ogni articolo di giornale, appare solamente, per qianto si sa, neliultimo quarto del secolo decimo quinto”, i.e., “The current use of two virgolette, in their old form as two small lines, between the two names of the concerned accounts in every Journal entry, appeared first, as far as it is known, in the last quarter of the 15th century.” La Ragioneria, second edition, Milan, 1916, Vol. Ill, p. 376. Actually, it seems that both vertical and slanting lines were used. In the set of entries included by Domenico Manzoni in his Quaderno doppio col suo giornale, two slanting lines are used before the term To to sepa

Another typographical anomaly due to printing circumstances appears in Chapter 12. When Pacioli explains in Chapter 14 how to show that Journal entries have been posted to the Ledger, he says: “An as of one Journal entry you post two to the Ledger, you will draw two transverse lines on the Journal entries as you post them. That is, if you post first the debit entry, you will draw the line at the beginning of the entry, thus showing that it has already been recorded on the debit side of the Ledger. And if you post the credit entry, you will draw the line at the end, on the right hand side, where the entry ends, to show that you have already posted it to the credit side of the Ledger.”4 Then, he adds: “These lines are as shown above in the first Cash entry, one of them is called the debit line and the other the credit line,”5 referring to an entry debited to the Cash account and credited to the Capital account provided as an example to explain how the first entry of the Inventory should be posted to the Journal.

However, in this entry (which appears in Chapter 12), there is no line across the body of the entry. Instead, in the left margin of the text, there is a sentence written vertically which says: “debit line.”6 No doubt, the typographical difficulty of drawing a line across the letters in the printed text led the printer to adopt this solution. Yamey also mentioned this typographical diffi

rate the debit and credit accounts. The same is done in Alvise Casanova’s work Specchio lucidissimo and in Angelo Pietra’s Indrizzo degli Economi, printed in Mantua in 1586. By contrast, in his two books Ein Teutsch verstendig Buchhalten, published in Nuremberg in 1531, and Buchhalten, zwey kiinstliche und verstendige Buchhalten, published in Nuremberg in 1546, Johann Gottlieb uses precisely the two vertical lines adopted by Pacioli in his Treatise to separate the wording of the debit and credit accounts in the Journal. Wolffgang Schweicker does the same in his work Zwifach Buchhalten, sampt seinem Giornal, des selben Beschlus, auch Rechnung zuthun etc., printed in Nuremberg in 1549 by Johann Petreius. Schweicker explains that he was living in Venice when he wrote his book.

4 “E cosi come duna de giornale ne fai 2 al quademo, cost a quella partita che del giornale levi fared doi righe a traverso so che vai levando; doe, se prima tu la metti in dare, prima farai una riga atraverso verso al principio de la partita, che dinota esser posta in dare al quademo, e si la metti in havere… farai laltra depennatura, verso man dextra, dal canto dove ftnesci la partita, che denotara esser messa in havere”.

5″Le qual linee staranno come disopra in questo vedi figurato a la partita prima dela casa, luna ditta linea de dare e laltra de havere”.
6 “Linea del die dare.”
culty in the article in which he discussed the previous one [Yamey, 1978].

In this same chapter, Pacioli explains how to cancel entries in the Memorandum after posting them to the Journal by drawing a transverse line to cross them out. But he warns: “And if you do not wish to draw a line across the entries, you shall tick the first letter of the entry, or the last one, as it was done at the beginning of this entry.”7 However, this tick mark does not appear anywhere.

The following observation does not refer to a typographical anomaly and is not even a real error. It is a simple curiosity or inaccuracy in the author’s explanation. In Chapter 16, he describes the way to post stocks of goods owned by the merchant from the Inventory to the Journal. The example given to illustrate this case is ordinary ginger in bulk which is the seventh entry in the Inventory. The previous entry, which is illustrated with an example, is the second one in the Inventory, i.e., jewels of various types. Pacioli assigns to both accounts the third folio of the Ledger. He warns and even recommends in various passages, as it was customary at that time, to use the same folio of the Ledger to keep more than one account when the accounts in question are not expected to originate much movement and will, therefore, not require more space. However, it clearly seems exaggerated to presume that six accounts (2 through 7) can be included in the same folio.

LINGUISTIC OBSCURITIES

In this section, I shall describe a few ambiguities and obscurities of Luca Pacioli’s Treatise which are difficult to understand and interpret. Some of them are obviously related to accounting or commercial issues but, it seemed to me, that the difficulty is essentially of a linguistic rather than technical nature. For this reason, these anomalies have been separated from the accounting, banking or commercial ones and are included in this section, although this criterion can, of course, be discussed.

The first difficulties of this type appear in Chapter 3, where there are several expressions whose meaning could not be clearly established and a few curiosities. For example, it is curious to observe that Pacioli uses the term goie or gioie, i.e., jewels, to describe precious stones.

In this same Inventory entry covering jewels, Pacioli includes some rubini coculegni that a few translators interpret as conical rubies. Carlo Antinori points out, however, that they could be rubies coming from Cochin, in the East Indies, on the Malabar Coast.

Another curiosity which has intrigued scholars in this chapter is the use of the word pironi instead of forchette to designate forks. Pirone is a word of Greek origin which has given its name to the fibula bone in French and Spanish. Researchers cannot understand how it came to be used in Venice with the meaning of fork, since the current meaning of this word in modern Italian is lever, bar, pin, handspike or bolt. In any case, Jager, the

Ernst Ludwig Jager, who did the first translation of the Treatise to a foreign language in: Lucas Paccioli und Simon Stevin, nebst einigen jiingeren Schriftstellem iiber Buchhaltung. Skizz&n zur Geschichte der kaufmannischen, staatlichen und landwirtschaftlichen Buchfiihrung, Stuttgart, 1876, translates the word as jewels, KLeinodie. In contrast, Balduin Penndorf: Abhandlung iiber die Buchhaltung 1494. Nach dem italienischen Original von 1494 ins Deutsche ubersetzt und tnit einer Einleitung iiber die Italienische Buchhaltung im 14. und. Jahrhundert und Paciolis Leben und Werk versehen von. . . , Stuttgart, 1933, already translates it as precious stones, Edelsteine. John B. Geijsbeek: Ancient DoubleEntry Bookkeeping. Lucas Pacioli’s Treatise (A.D. 1494 — the earliest known writer on bookkeeping) reproduced and translated with reproductions, notes and abstracts from Manzoni, Pietra, Mainardi, Ympyn, Stevin and Dafforne, Houston, 1914, translates the term as jewels. Pietro Crivelli: An Original Translation of the Treatise on DoubleEntry Bookkeeping by Frater Lucas Pacioli. Printed in Italian Black tetter, and Published in Venice in 1494. Translated for the Institut of BookKeepers Limited by… , London, 1924, also translates it as jewels, the same as R. Gene Brown and Kenneth S. Johnston: Pacioli on Accounting, New York, 1963, whereas Robert Haulotte and Ernest Stevelinck: Luca Pacioli. Sa vie. Son oeuvre, Vesoul, 1975, translate the word as precious stones, pierres precieuses. This translation is also adopted by Ramon Cardenas in his version of Luca Pacioli work: Summa de Arithmetica, Geometria, Proportioni et Proportionalita .. . Distinctio Nona, Tractatus XI, De Computis et Scripturis (De las Cuentas y la Escritura). Venecia, 1523, 2″‘ Edicion. Version y arreglo al espanol: Ramon Cardenas C; Traduccion, prologo y revision: Dr. Giorgio Berni (Second Edition), UANL, Monterrey, N. L., Mexico, 1991. Carlo Antinori: “11 Trattato dalla ‘Surama’ del Paciolo. A cura di . . . “, in Summit. Gli speciali di Summa. Supplemento al n. 40 di Summa, November 1990, translates it, on the contrary, as gioie, jewels, in his version into modern Italian.
‘Jager translates the term coculegni as Kegelformig, conical, whereas Penndorf translates it as dickgeschliffen, an usual type of cutting in old times, based on Manzoni’s expression cuogolo. Brown and Johnston, Haulotte and Stevelinck and Geijsbeek do not mention the term. Crivelli and Cardenas leave it untranslated.

first translator of the Treatise into a foreign language, already translated the term correctly, using the word Gaheln, forks.10 Carlo Antinori obviously does the same in his version of the Treatise in modern Italian.

We also find in this chapter a word, vergini, which has caused some difficulties for translators. In his German version of 1933, Balduin Penndorf translates this term as Brasilholz, i.e., brazilwood, a type of wood that was used for red dyeing. R. Gene Brown and Kenneth S. Johnston do the same in their translation into English of 1963, calling it brazilwood. In most of the other translations consulted, the term is not translated — an example that I have followed in mine, although mentioning these observations in a footnote.11
10 Crivelli does not translate the term in the text. However in a vocabulary added at the end of his work, he attributes to this word the meaning of a peg.

“Crivelli leaves also the term untranslated, but in the vocabulary provided at the end, the meaning attributed to it is also brazilwood. Haulotte and Stevelinck leave it untranslated. Antinori calls it legno verzino, which actually means brazilwood. However, as Antonio Lopes dc Sa also observes in his comment to this paper, it is difficult to understand how people knew in Venice, in 1494, a product coming from a land which was incorporated to the crown of Portugal in 1500. Though it is known that navigators such as Vicente Yanez Pinz6n, the companion of Columbus, Alonso de Ojeda together with Americo Vespucio, and Diego de Lepe had visited the coast of Brazil, until the 22nd April 1500 it was not taken by Pedro Alvarez, Cabral for the king of Portugal. On this day, Cabral landed at Porto Seguro and called the land “Isla de la Vera Cruz” (Island of True Cross). This is surely what has compelled more than one translator to leave the term untranslated.

Nevertheless, we must not forget the fact that the name “brazil,” which comes from the Old German brasa, i.e., fire, seems to be older than American’s discovery and that the product itself, in the broad sense of red dyeing wood, was already known before this discover. Precisely, this wood gave its name to the land of Brazil. In fact, it seems that a tradition from the 13th and 14th centuries said that somewhere within the Atlantic Ocean there was a mysterious land where the forest produced a great deal of the dyeing wood used at that time to dye red; due to the color it gave, this wood was called brazilwood, (i.e., firewood). The cartographers of that time thought that this land was an island and located it in the middle of the Atlantic Ocean on the same latitude as the Land’s End Cape in England. The first people who arrived at Vera Cruz found plenty of red dyeing wood, so they thought they had discovered the true land of brazilwood; they began to call the land in this way and, eventually, the name Brazil prevailed over Vera Cruz. Consequently, it is possible that the verzino or brazilwood mentioned by Pacioli, although not true brazilwood as we know it nowadays, (that is, wood from the tree Caesalpina echinata) were a sort of red dyeing wood, for instance campeche wood (Haematoxylon campechianum), which grows on the Caribbean coasts, or sapanwood (Caesalpina sappan), which grows in India, etc. Moreover, one must not forget that some varieties of Caesalpina which also produce red dyeing wood grow in

Chapter 9 contains a passage whose interpretation has recently raised some doubts. This passage, which refers to time purchases, starts and concludes as follows: “E cosi quando tu facesse le tue compre a tempo, commo se costuma ale volte farsi de guati overo biade, vini, sali e curami .. . E cosi de liguati, o biade specificar tanto el migliaio, e tanto lo staro, o el moggio, o la corba dele biade, commo insul chiusi de peroscia si costuma, e de guati, al Borgo Sansepolcro nostro .. .”, i.e., “And thus, if you make time purchases, as people sometimes do when buying fodder grass or cereal, wine, salt and hides . .. The same occurs with fodder grass or cereal for which you will specify the price by unit of measure, so much the thousand pounds, the staro, the moggio or the basket of cereal, as it is customary in Chiusi of Perugia, or of grass, as in our Borgo Sansepolcro . .. “. The meaning of biade in modern Italian is indeed “fodder cereal.” To translate guati, I have adopted the interpretation usually given to this term, i.e., “grass” or “hay.” However, Pierre Jouanique has recently pointed out to me that in modern Italian the expression guado means “woad,” a plant whose leaves provide a tinctorial substance used as blue dye. The distinguished French accounting historian deduces that Pacioli did not refer to hay but to woad because it does not seem reasonable that hay should be sold in baskets. On the other hand, I myself must add that, although the translation of biade in modern Italian is, as we said, fodder cereal, there is a diminutive, biadetto, which is the blue pigment used by painters. It is thus possible that the two expressions used by Pacioli in this passage, biade and guati, may refer to tinctorial substances, as I explain in a footnote in my work. I have, however, retained the traditional translation.

The continuation of this passage also contains a term which has been incorrectly interpreted in all the translations consulted. The passage goes on as follows: “Al Borgo Sansepolcro nostro, Mercatello, Santangnilo, Cita de Castello, Furli, etc.”. This sentence has traditionally been translated in the following way: “As in our small market of Borgo Sansepolcro, Santangelo, Citta di Castello, Forli, etc.” However, Pierre Jouanique drew again the Antilles. In fact, the Tariffa de tutti costumi, cambi, monete, pesi, misure e usance di lettere di cambi e termini di dette lettere che ne paesi si costuma, e in diverse terre, which is included in the Summa as Tractatus XII of the Distinctio nona, mentions in folio 223 r° a vercino colombino, “which must be thick and red, of good color.” In this way, the term verzino used by Pacioli might possibly refer to a sort of red dyeing wood after all, even if it was not brazilwood proper.

my attention on the possibility that the word Mercatello did not refer to a small market but to the town of that name located on the Metauro River, precisely at the confluence of the Meta and Auro torrents which give rise to that river. I believe that the meticulous French researcher is absolutely right, considering that there is no reason to assume that the ortographic sign which separates nostro from Mercatello is placed there out of fancy. On the other hand, all the towns mentioned by Pacioli in this context are close to one another. The name of Santangelo may refer to two towns: Santangelo in Lizzola, near the coast and Pesaro, and Santangelo in Vado, on the same Metauro River, as Mercatello; Citta di Castello is near Sansepolcro, a little further south; and the most distant one, Forli, stands to the north, near Ravenna.

In Chapter 10, Pacioli mentions for the first time in his Treatise the “escripture menute” that some translators have translated as “small records” or “minor records.” This expression reappears later in various parts of the Treatise, though not in relation to short or scarcely important records. It appears that Pacioli used this term to refer to “loose records,” as opposed to account books which formed a bound volume.

Although the meaning of an expression used by Pacioli in Chapter 17 has been more or less correctly interpreted, it has plunged almost all translators into perplexity. Referring to the need to record everything and not to rely on memory, the distinguished Franciscan monk says: “Formarai la partita in giornate e quaderno per ordine, depennando e segnando in tutti lochi, che non tescordi, perche al mercante bisogna altro cervello che de beccaria.” The most current translation of the sentence has been: “For the merchant needs a different brain to that of a butcher.”13 I believe the key to a correct interpretation can be

Jager translates the term as Heine Handschriften, i.e., small handwritten records, practically the same as Penndorf who calls the scripture menute kleine Schriftstiicke. Geijsbeek avoids the problem, calling them other instruments of writing. Crivelli translates them as trifles, the same as Brown and Johnston. Haulotte and Stevelinck also avoid the problem, translating the expression asmissives, and Cardenas calls them escrituras menores, minor records. Antinori translates them literally as scritture minute.

In effect, Jager translates this passage as follows: “Denn dem Kaufmann istein besserer Verstand von Nb’then als dem Metger.” Penndorf adopts a similar version: “Weil dem Kaufmann ein anderer Verstand notig ist als dem Fleischer.” Geijsbeek follows the same line in his translation: “Because the merchant must have a much better understanding of things than a butcher,” the same as found in Carlo Antinori’s translation into modern Italian: “Poiche al mercante occorre altro cervello di quello che si vende nelle beccherie.” Guided by this interpretation, I have translated the complete passage as follows: “You will have to post them all to the Journal and to the Ledger, one by one, in order, duly canceling and indicating all the things so as not to forget them, for the merchant needs a live brain and not those sold by butchers,” which is certainly a little freer version than Antinori’s.

At the end of the last paragraph of Chapter 32, there is an expression, “Ideo etc.” which has usually been omitted by translators. Pierre Jouanique points out to me, however, that Ideo introduces a request to intercede. Elsewhere, Pacioli asks his readers to pray for him. In this case, he writes only the first word of the final formula of the Confiteor in Latin: Ideo precor . . . et vos fratres, orare pro me ad Deum Dominum nostrum, i.e., “I thus beg … and you brothers to intercede for me with God our Lord.”
In Chapter 35, the following passage on how to dispatch the post has also caused doubts and difficulties to the various translators:

“Haverai in tuo studio overo scritoio una tassca, nela quale reporrai lettere che li amid te dessero che tu con le tuoi mandasse, alora se did che la mandi a roma, mettila in tasca di roma, e se a firenca in quella de firenga, etc. E poi nel spaciare del fante pigliale con le tuoi al tuo respondente in quel tal luogo le manda, perche el servire sempre e buono e anche susa dar suo beveragio per esser servito. Atorno esso cinta compartita come si fa in piu taschette, doe in tante quante sonno le terre e luoghi in le quali fai le toe facende, come diciamo: Roma, Firenge, Napoli, Milano, Zenoa, Lion, Londra, Bruga, etc. E sopra ditte taschette per ordine scriverai il suo nome, doe a luna dirai Roma, alaltra Firenga, etc., in le quali poi reporrai le lettere che per quelli luoghi te fossero mandate da qualche amico che la mandasse.

Crivelli: “For the merchant requires a different brain to that of a butcher.” Brown and Johnston attribute a similar meaning to this expression: “The businessman must understand things better than the butcher.” Likewise, Haulotte and Stevelinck interpret it as: “Car un marchand doit montrer plus de comprehension des choses qu’un boucher,” and Cardenas as: “Porque el comerciante necesita otros sesos que no sean los del carnicero,” i.e., “Because the merchant needs another brain than that of a butcher.”

The difficulty lay in making the part starting with Atorno agree with the preceding one. I have translated this controversial part in the following way: “With respect to the above, you could also have a belt or panel with as many pockets as business places . .. ,” i.e., have a belt or panel with various pockets instead of a separate bag for each business place, although this translation can also be questioned.

In the last section of the Treatise, which is unnumbered and comes immediately before the examples of Ledger entries provided at the end of the work, there is an expression which could not be interpreted satisfactorily: “lane di limistri.” Some translators have not translated the word limistri. However, in his English version of the Treatise, Crivelli translates this expression as mixed wool, the same as R. Gene Brown and Kenneth S. Johnston. In contrast, Balduin Penndorf considers it to mean exactly the opposite and translates it into German as reine Wolle, i.e., pure wool.15 Carlo Antinori believes Limistri can be the name of the town where the wool originated, suggesting it was the Irish town of Limerick. I have chosen to leave the word untranslated with a reference to the various interpretations in a footnote.

In his translation, Jager avoids the problem, considering the second part as a simple repetition of the first. More precise, Penndorf says: “Man kann die Briefe auch im Kreise herum auf mehrere Taschen verteilen .. .”, i.e., “The letters can also be distributed in several bags in a circle … “. Geijsbeek also tries to be faithful to the text, although not quite successfully, as it seems, saying: “You should have several little compartments, or little bags . . . “. Crivelli gives an original interpretation: “By the messenger who is belted with the parcel of letters which is made up of several pockets . . . “.

A similar interpretation is given by Brown and Johnston: “The messenger wears a belt with several pockets for carrying letters.” Haulotte and Stevelinck introduce a small difference: “Le sacdu courrier peut comporter autant de petits compartiments ou poches …”, i.e.,

“The mail bag may be divided into as many small compartments or pockets . . .

“. This translation is also adopted by Cardenas: “Respecto a la valija, estaird dividida en tantas pequenas bolsas . . .”, i.e., “With respect to the bag, it will be divided into as many small pockets …” and Antinori: “// sacco del corriere pud avere tanti piccoli compartimenti o taschette . ..”. This interpretation could be plausible but I did not dare to adopt it because I do not clearly understand how this way of delivering the mail could work and also because this description is not really in accordance with the following explanations.

Jager sincerely puts a question mark instead of translating limistri, although it seems that he is also inclined to think that it is the place of origin. Geijsbeek also leaves the term untranslated, whereas Haulotte and Stevelinck omit the word. Cardenas leaves it untranslated, explaining in a note that “Alparecer, no ha sido posible encontrar el verdadero significado de dilimistri,” i.e., “It has apparently been impossible to ascertain the real meaning of dilimistri.”

TECHNICAL OBSCURITIES AND AMBIGUITIES

This section deals with the obscurities, inaccuracies and ambiguities which effect more directly explanations on commercial, banking and, above all, accounting customs and practices.
The first difficulty is chiefly conceptual. It appears in Chapter 1 and refers to the three things basically needed by anyone who wishes to engage in business activities. According to Pacioli, the main one is “la pecunia numerata e ogni altra faculta sustantiale, Juxta illud phy unum aliquid necessariorum (sic) est substantia. Senga el cui suffragio mal si po el manegio traficante exercitare.” Leaving aside the error of printing necessariorum instead of necessarium, this passage has caused serious difficulties to translators and scholars because nobody knew how to interpret the concept of sustantia or sustantiale in this context. In my Spanish version, I have translated the passage as follows: “The main of them is cash money and any other patrimonial good which can be converted into money, since without money or means of payment, it is difficult to negotiate. As the Philosopher already said: only one thing is necessary: the substance, that is, the patrimony.”

I based this translation on Pierre Jouanique’s interesting analysis of the use of the Latin term substantia by Pacioli in this juridical and commercial context. This term is the translation of the Greek word ousia used by Aristoteles — who is “the Philosopher” referred to by Pacioli — to designate the essential part of things, i.e., what remains in things that change. According to Jouanique’s interpretation, the term substantia or patrimony refers to what remains to the abstract global concept of all property owned as a whole while its specific components (money, goods, real state, etc.) change [Jouanique, 1987, p. 253]. On the other hand, it should be remembered that in modern Greek the concept of patrimony is precisely designated by the word periousia. In any case, this interpretation is totally familiar to German scholars because one of the meanings of Substanz is still that of real or actual capital. The expression “von der Substanz zehren” means, in financial slang, “to live off the capital” or “to eat up one’s capital.”

16 According to what has been said, Jager correctly translates the expression “e ogni altra faculta substantiate” as “jene andere Vermogenssubstanz,” i.e., “and any other good or patrimonial capital.” Penndorf does the same. Geijsbeek finds it more difficult and says only: “The most important is cash or any equivalent,”

Another complicated expression in this sense is found in Chapter 3 where, referring to the precautions to be taken when entering deposits made in banks and credit entities, it is said that: “E nota el milesimo che respondano a tempo per tempo acio sappia quando vengano li so pro, e quanta per cento respondino.” Although the meaning of the expression seems clear to all or almost all translators, a number of them had some difficulty in finding the correct translation. My own version reads as follows: “Also note the year in which the deposit falls due and the maturity dates, so that you may always know when interest is due and what percentage you should receive.”

without going more deeply into the subject. Crivelli does not understand the expression either and says: “Or any other substantial power.” Brown and Johnston get nearer to the true meaning of the sentence, translating it as: “The most important is cash, or some equivalent economic power.” Haulotte and Stevelinck translate the expression in the narrow sense: “La principals chose est la monnaie metallique ou tout autre moyen de paiement,” i.e., “The main thing is coin or any other means of payment.” Cardenas translates it literally: “La principalisima es el dinero contante, asl como de otros bienes sustanciales,” i.e., “The very main thing is cash money, as well as other substantial goods.” Antinori gives a similar interpretation: “La principale e la moneta contante e ogni altro valore corrente,” i.e., “The main thing is cash money and any other current value or good.” In my opinion, the importance of the sentence lies in the expression “and any other patrimonial good” and the sentence can be completed in the sense that Pacioli apparently wanted to stress, by adding, as I did, “which can be converted into money.

“Interpreting correctly the meaning of the expression, Jager translates it as: “Erw&hne auch die Jahreszahlen, welche dem Verfall der Zinse entsprechen, damit man weiss, wann letztere verfallen, ferner wie viele Procente dieselben betragen,” i.e., “Also indicate the year in which interest is due, so that you can know the maturity date and the percentage to be applied.” Penndorf attributes to these words the same meaning: “Bemerke auch die Jahreszahlen, die der Falligkeit entsprechen, damit man weiss, wann die Zinsen Fdllig sind, und wieviel Prozent sie betragen.” Geijsbeek is a little less accurate: “And you must also see that dates are put down precisely so that you know when everything falls due arid what the per cent is.” Crivelli is even more inaccurate, saying: “Take note of the date on which they reply to you from time to time, so that you may know what is due to you and what percentage they are answerable for.” Brown and Johnston translate the expression in the same sense: “Carefully note the dates of their correspondence, so that you know the amount due you and what percentage they are answerable for.” Haulotte and Stevelinck provide, in my opinion, the most correct translation among those reviewed up to now: “Je note aussi quand le d&pdt fut effectue et pour quelle duree afin d’en connaltre le jour de I’ichiance, ainsi que le pourcentage qui doit le retribuer,” i.e., “I also note when the deposit was made, and for how long, in order to know the maturity date, as well as the percentage to be applied to it.” Cardenas is not sure that the word millesimo used by Pacioli means year. For this reason, he leaves it untranslated, although he indicates in a

In Chapter 6, an expression used throughout the treatise appears for the first time. This expression has apparently been misunderstood by some translators. I refer to the expression cavar fora, i.e., to take out. When talking about the entries made in the Memoriale, the Memorandum, it is said that: “In questo tale (the Memorandum) non fa caso a che moneta si cavi fore, commo nel giornale e quademo, che di sotto se dira, etc. El quadernieri asetta tutto poif lui quando de li pone in giornale.” The sentence refers to the cash amounts of operations that had to be carried to the money column, i.e., out of the body of the entry.18 The expression “sacar fuera” was used with the same meaning by Castilian bookkeepers in the sixteenth century. In this case it is explained that, when posting the entries to the Memorandum, the kind of money (i.e., ducats, pounds, pennies, etc.) which was carried to the money column did not matter. The contrary occurred with the Journal and Ledger where the money of account always had to be the same so that homogeneous money columns could be added up. This did not matter in the Memorandum because the bookkeeper would convert them all into the required money of account when posting the entries to the Journal. It should be pointed out that we are exclusively referring to the money column since the money in which operations were actually carried out was obviously recorded in the entry’s explanation.19
note that it apparently represented the last two figures of the corresponding millenium, i.e., the year referred to and, by extension, also the date. However, his translation basically corresponds to the meaning of the expression: “Y anota el millesimo que corresponda en cada caso, los porcientos (reditos) que te corresponden, etc.”, i.e., “And note the millesimo which corresponds in every case, the percentage (yield) applicable to you, etc..” Antinori’s translation is, of course, perfect: “Nota anche quando il deposito fu effettuato e per quale durate, per sapere quando siano riscuotabili gli interessi e a quale percentuale corrispondano,” i.e., “Also note when the deposit was made and for what period of time to know when interest is due and what percentage is to be applied.

18 In her Glossary of Medieval Terms of Business. Italian Series 12001600, Cambridge, Mass., The Medieval Academy of America, 1934, p. 71, Florence Edler interprets the expression “cavare fuori” with this same meaning and quotes, moreover, as an example the corresponding text of Luca Pacioli in folio 200 r.

“Jager did not understand at all this passage that he translates as follows: “Denn beziiglich dieses Buches ist es nicht, wie im Journale und Hefte, gteichgiltig, was fitr Miinzen man ausgiebt oder einnimmt” i.e., “Because in this book, the kind of money used for payments or collections is not unimportant, as in the Journal and Ledger.” The translator interprets that the expression cavar fora means to spend, to pay. In contrast, the meaning given by Penndorf to the

In Chapter 9, there is another term which has also created much confusion among most translators. When describing the forms of payment to be used to purchase merchandise, Pacioli mentions payment “per asegnatione de ditta.” Considering that today ditta means “business firm” in Italian, it is not surprising that some translators have translated the expression as “drawing a bill of exchange against a business firm.” This is how it has been translated for instance by Carlo Antinori or Ernst Ludwig Jager who uses the expression “Anweisung einer Firma.” I do not believe this translation is correct. Others have limited themselves to translate it as draft, bill of exchange or payment order.20 This is more correct, though the translators who used

expression is more correct: “Denn in diesem Buche ist die Geldsorte, die du auswirfst, nicht so von Bedeutung wie im Journal und Hauptbuch,” i.e., “Because in this book the kind of money recorded in the margin is not so important as in the Journal and Ledger.” Geijsbeek understands that it is not necessary to reduce the monies to a single money of account but he does not get the meaning of cavar fora: “As far as this book is concerned, it is not as important to transfer to standards the various kinds of coin handled as it is with the journal and ledger.” Crivelli does not understand it so well: “Because in this book it is not necessary to separate the monies as in the Journal and Ledger.” Brown and Johnston do understand the basic meaning but, the same as Geijsbeek, they avoid the problem of translating cavar fora: “It is not necessary to standardize monies in this book, although it is required in the Journal and Ledger.” Haulotte and Stevelinck do the same: “Dans ce livre, il nest pas necessaire de reduire a. une commune unite monetaire les diverses especes de monnaie, comme e’est le cas pour le Journal et le Grand Livre,” i.e., “In this book, it is not necessary to reduce the various kinds of money to a single money of account, as in the Journal and Ledger.” Cardenas also follows the same line: “Porque en este libro no tiene caso en que monedas se anoten las transacciones; no pasa lo mismo con el Diario y el Mayor,” i.e., “Because in this book, it does not matter in which money transactions are recorded, as opposed to the Journal and Ledger.” Although Carlo Antinori knows perfectly the meaning of cavar fora, he does not consider it necessary in this case to specify the question and simply translates as the previous translators: “Perche in questo libro non e necessario ridurre a una comune unita monetaria, tutte le specie di monete come invece si deve fare nel Giornale e nel Libro Mastro.

20Penndorf provides an interesting interpretation, although he translates “asegnatione de ditta” as “Anweisung weiner Biirgschaft,” i.e., delivery of a guarantee. Based on Ehrenberg (Das Zeitalter der Fugger, Jena, 1922, II, p. 124), to him the word ditta means Zahlungsversprechen, promissory note, and in this case, he believed that the expression used by Pacioli referred to the guarantee given by a bank in relation to the payment order drawn by a client against his current account. This interpretation cannot be totally discarded, although it seems exceedingly complex. Actually, ditta was a simple payment order against a bank, an antecedent of the modern check, as explained in another note. Geijsbeek translates the expression as draft, without going into details.

Crivelli this term do not seem to have actually understood the meaning of the expression. Even before the times of Luca Pacioli, the word ditta originally had a perfectly determined meaning: it was a verbal payment order — hence the name ditta — that a client gave in person to his bank to pay against his current account a cash amount to a given beneficiary who was also present.21 Later, payment orders evolved to written instruments that gave rise, in the course of time, to modern checks. However, in Italy and even in Catalonia, the name ditta continued to be used for this purpose for many years [Conde y Delgado de Molina, 1988]. Therefore, I understand that payment “per asegnatione de ditta,” as mentioned by Pacioli, should be translated as draft or payment order against a bank and this is how it appears in my version.

bothers to specify a little further and translates it as “a firm’s draft.” Brown and Johnston, on the contrary, translate it only as draft. Haulotte and Stevelinck use, however, the expression “lettre de change tiree sur une maison commerciale,” i.e., “bill of exchange drawn on a trading house.” Cardenas leaves it untranslated in the text but correctly explains in a note: “Puede traducirse como ‘orden de pago’ o ‘giro’ a cargo de un banco, previo deposito expreso, de acuerdo con una prdctica de la epoca,” i.e., “It can be translated as ‘payment order’ or ‘draft’ against a bank, after making a deposit in same, as it was usual at that time.

This is how it is explained, among others, by Federigo Melis: “una girata oraie, pronunciata dal beneficiario alia presenza del trattario, a somiglianza diquanta avveniva fra girante e giratario di conto presso le banche di giro.” See his work “Una girata cambiaria del 1410 nell’Archivio Datini di Prato,” in Federigo Melis: La banco pisana e le origini della banca moderna, Florence, 1987, p. 303.

An interesting and wellknown controversy arose precisely on this question some years ago between Abbot P. Usher and Raymond de Roover, on one side, and Federigo Melis, on the other. The first two authors thought that in Italy, in the 14th century, all payment orders to banks had to be transmitted verbally and necessarily required the presence of both parties. On the contrary, Melis defended the idea that, although this was the current usage, it did not exclude the existence of written orders delivered to the bank by messengers, or even by the
beneficiaries themselves, without requiring the presence of the bank’s client.

In his kind observations to this work, Carlo Antinori reasserts that, in his opinion, “assegnatione de ditta si interpreta come ordine di pagamento a una ditta, mediante lettera di cambio” of which, as he points out, Luca Pacioli provides an example in folio 167 v° of the Summa. And this without taking into account, as he says, that if it were not so “la forma di pagamento mediante ordine con lettera di cambio non sarebbe stato contemplata perche non indicata.” Indeed, Antinori is right on this point but it should not be forgotten that, in the fifteenth and immediately following centuries, the bill of exchange was not used as a payment instrument among merchants, unless payment was to be made abroad and in a
currency different from that used in the town where it was drawn. On the other hand, Pacioli does not seem to use in his Treatise the expression ditta, as assumed by Antinori, in the current sense of firm, concern or company. Finally,

An observation made by Pacioli in Chapter 12 with respect to the valuation of assets has caused much perplexity to more than one scholar. Pacioli says: “Ponendoli (to the goods) tu per te un comun pregio. E fallo grasso piu presto che magro. Cioe, se ti pare che vaglino 20, e tu di 24, etc., ado che meglio te habia reuscire el guadagno,” i.e., “And you will value them (the goods) according to your own judgment at their current value that should be rather high than low. For instance, if it seems to you that a thing is worth 20, value it 24, and you will thus obtain a greater profit.” If this observation is considered a formal accounting valuation rule, it is really disconcerting. No wonder that several authors have severely criticized this statement, attributing it to a lapsus of the author.23 In my opinion, however, we should not give so much importance to what I believe to be a mere subtlety of a crafty merchant which has nothing to do with an accounting overvaluation criterion of assets.

If you try the expression assegnatione de ditta does not appear at all in the treatise on exchanges mentioned by Antinori, nor is there any reason to assume that this expression could be synonimous with lettera di cambio. In effect, Luca Pacioli devotes folios 167 r” (there is a typographical paging error, since the folio is numbered 168 instead of 167) to 173 v° of his Summa to the Tractatus quartus none distinctionis under the title De cambijs seu cambitionibus that he translates in the general index as Dechiaratione de tutte sorte cambi, cioe reale, secco, fittitio e come o vero diminuto, qual di loro sea licito e laudabile secondo la sancta chiesia e commo se intenda ciascuno secondo luso mercantesco. In this treatise, Pacioli explains the four types of exchanges he distinguishes, adding numerous practical examples. However, when he refers to the documentary instrument of exchange, he always mentions the lettera di cambio.

23Among them, Carlo Antinori says that it is “un consiglio errata,” i.e., “a wrong advice” and that “si tratta di un autentico invito all’annacquamento del capitate, anche se trattandosi di valutazione iniziale non si migliora il guadagno futuro, anzi lo si disminuisce,” i.e., “it is a real invitation to overvalue the capital, besides the fact that, as it is an initial evaluation, the future gain is not imporved but reduced.” (“II Trattato dalla ‘Summa’ del Paciolo. A cura di Carlo Antinori,” in Summit. Gli speciali di Summa. Supplemento al n. 40 di Summa, November 1990, p. 7). Jager briefly observes in his translation: “Diess ist heut zu Tage nicht mehr erlaubt,” i.e., “This is not allowed today.” Penndorf also feels the need to remark in a footnote: “Die Praxis befolgte jedoch den richtigen Grundsatz des Niedrigstwertes,” i.e., “However, the principle of the lesser value was correctly followed in practice.” Cardenas also makes a remark in a note, besides putting a question mark between brackets in the text. In his note, after suggesting several possible explanations, he concludes: “Por tanto, se estima que Paciolo estd sufriendo en este caso una confusion de conceptos, lo cual se atribuye a que, como se sabe, Paciolo no era contador,” i.e., “Therefore, it seems that Pacioli was suffering a conceptual confusion in this case due to the fact that, as it is wellknown, he was not an accountant.”

to value your goods at a rather high price, you will not yield so easily to the temptation of selling them at a scarcely remunerating price. According to this interpretation, in my translation, the last part of the passage appears as follows: “And in this way it will be easier for you to make a profit.” In any case, it is clear that this too is a very subjective interpretation. However, it is necessary to’ point out that Pacioli’s words seem to refer exclusively to goods whose purchase price is not known, when calculating the Inventory, because they were bought before starting to keep the relevant accounts.

The title of Chapter 13 refers to the Index of the Ledger in the following way: “E del suo alfabeto, commo se debia ordinare, ugnolo e dopio,” i.e., “And of its index, how it should be ordered, single or double.” In the chapter itself, however, only a short reference to this double way of ordering can be found without any clear explanation, when Pacioli says: “Net qua! (the index) porrai tutti debitori e creditori per le lettere che comencano con lo numero dele sue carti, doe quelli che comengano per a in a, etc., e del dopio alfabeto,” i.e., “In which (the index) you will put down all debitors and creditors, with the number of their folios, by their first letter, that is those that start with an A under A, etc., and of the double alphabet.” It is possible that this last sentence is an incomplete one as it also occurs with the last sentence of Chapter twentysix. In any case, it does not seem to make sense and this is, no doubt, the reason why most translators have omitted the last part of the title and the translation of the mentioned reference.24 At any rate, the double option indicated by

24This is, for instance, what Carlo Antinori does. He entitles this chapter: “Del terzo ed ultimo libro principale mercantile detto MASTRO, come deve essere tenuto col suo REPERTORJO,” and omits any mention of the reference made in the text. Haulotte and Stevelinck do exactly the same. Jiiger maintains the complete title but does not mention the reference in the text. In contrast, Penndorf translates it literally, which is not much help to understand the sense, although he explains correctly in a footnote: “Doppelt, weil auch innerhalb eines jeden Buchstabes die Namen alphabetisch folgen,” i.e., “Double because the names appear in alphabetical order also under each letter.” Geijsbeek also translates the complete title but omits the reference in the text. Crivelli makes a serious mistake in his translation of the title: “Of the Third and last Principle Mercantile Book called the Ledger, How it is to be kept Single without, or Double with its Alphabet” and again in the text after the mentioned passage: “It will be best to sign the double Alphabet (Ledger)…” Brown and Johnston also make the same mistake in their translation of the title, surely induced by Crivelli’s translation, but they do not make any reference in the text. Cardenas translates the complete title and mentions the reference in the text but his explanation does not make

Pacioli answered a fact that was already explained by Karl Peter Kheil in his analysis of Jehan Ympin’s text. In the single index, only one page of the book is used for each letter of the alphabet. On this page are recorded the accounts whose heading or holders’ Christian name starts with that letter, indicating immediately after the folios where the respective accounts appear in the Ledger. On this page, the headings of the accounts are written without any order as the accounts are opened in the Ledger. In contrast, in the double index, all the letters of the alphabet are listed on the page or double page of the book used for each letter, leaving a blank for each of them, thus forming a kind of alphabetical subdivision under each letter. The accounts are then recorded in the corresponding subdivision according to the first letter of the surname, if it is a personal account, or to the second letter of the heading, in other cases.

In this same Chapter 13, Pacioli explains how to keep the Ledger and uses an expression: faciata, which appears later on several occasions with the same meaning and which does not seem quite clear to me. In modern Italian, apart from the architectural meaning of front, any face of a building, facciata also means page, side (of a sheet). For this reason, almost all translators translate it as “page.” Interpreting the word according to the meaning of the sentence in which it is included and taking for granted that Pacioli used two facing pages to keep the Ledger accounts,261 gave to the word faciata the meaning of Ledger

much sense: “… comenzando por A, en la A, del propio alfabeto,” i.e., “… if it begins by A, under A of the alphabet itself.

More recently, Basil S. Yamey has studied the Ledger indexes in his article: “The Index to the Ledger: Some Historical Notes,” in The Accounting Review, vol. 55, no. 3, July 1980. Jose Maria Gonzalez Ferrando has also referred to this subject in passing, in his usual detailed and meticulous style, in his work: “Bartolome Salvador de Solorzano, adelantado de la ‘Contabilidad Aplicada’ en Espana,” in Revista Espanola de Financiacion y Contabilidad, vol. XX, no. 68, JulySeptember 1991, p. 727 f. In his book Nieuwe Instructie Ende bewijs der loofelijcker Consten des Rekenboecks ende Rekeninghete te houdene nae die Italiaensche maniere, Antwerp, 1543, Jehan Ympym provides an example of double index.

However, Pacioli does not specifically write anywhere in his Treatise that in the Ledger an account is written on two facing pages. Basil S. Yamey, too, notices this fact in his comments to this paper. In any case, it seems that the traditional form to keep the Ledger in the early Venetian practice was precisely to write the accounts on two facing pages, as we can see for instance from the words of Paliano di Folcho da Firenze used as heading of his Ledger written in double page or folio in my translation. I shall return to the subject later in another context. Specifically, Pacioli’s passage reads as follows: “E in la pritna sua carta, dentro, porrai debitrici la cassa: si commo ella e la prima nel giornale, cosi deve essere prima nel quademo. E tutta quella faciata si costuma lasarla stare per ditta cassa, e in dar ne in havere non si pone altro, e questo per che la cassa se manegia piu che partita che sia,” and my translation is: “In the first folio, on the inside face, that is on the reverse, you will put down the Cash, on the debit side, since as it is the first entry in the Journal it should also be the first one in the Ledger. And these two facing pages are usually reserved to Cash. Thus, nothing more is to be recorded neither on the debit side, nor on the credit side. This is done so because the Cash is used more than any other account.”

Also in Chapter 13, Pacioli describes the lines to be drawn in the Ledger and there seems to be a small ambiguity in this respect because it is sometimes not clear whether the word riga is used in the sense of line or column. At any rate, it is explained that two lines must be drawn before the space conresponding to the body of the entries to indicate the date of each of these entries so as to locate them easily: “E dinance farai 2 righe per potere mettere li di de mano in mano, commo ne li altri quaderni hai visto che piu non mi stendo in questo, etc., per poter trovar presto le partite.” In Chapter 15, however, when explaining that in the Ledger the date is not written in the upper part, at the
1382: “…e scriverollo alia viniziana, cioe ne I’una carta dare e di rimpetto Vavere . . . ,” i.e., “… and I shall write it in the Venetian fashion, that is, the debit on one page and the credit on the other. . . ,” or from the words of Americho di Giovanni di Americho Benci, citizen and merchant of Florence, at the beginning of his Ledger of 1459: “… il quale se terra alia viniziana, cioe da una faccia il dare et dall’altra Vavere . . .,” i.e., “… which will be kept according to the Venetian model, that is, the debit on one page and the credit on the other . . .”. Quoted from Fabio Besta: La Ragioneria, quoted work, Vol. Ill, pp. 328 f.

27 Jager translates: “Und man pflegt jene ganze Seite fur besagte Cassa leer zu lassen,” i.e., “And it is customary to leave the whole page empty to the mentioned Cash.” Penndorf says exactly the same. Geijsbeek as well: “It is customary to reserve the whole of the first page to cash.” Crivelli does not introduce any significant change: “The whole page must be left to cash.” Neither do Brown and Johnston: “Reserve the entire first page for Cash.” Haulotte and Stevelinck follow the same line: “D’habitude, on reserve toute la page a la Caisse,” i.e., “The whole page is usually reserved to Cash.” Cardenas uses the term sheet instead of page: “Y toda la hoja de’jala para la Caja,” i.e., “And leave the whole sheet to Cash.” Antinori follows the general criterion: “Abitualmenta si riserva tutta la pagina alia Cassa.”

HerndndezEsteve: Obscure Points ofDe Computis Et Scripturis 37
beginning of the page, as in the Journal, because entries in a Ledger account will usually correspond to different dates, it is specified that the dates will be included in the body of the entry: “Ma dentro dela partita.”26 This is what appears in all the examples of Ledger entries provided in the Treatise, including the ones provided in the appendix which are formulated following the Tuscan and not the Venetian model as the previous entries do. Later on, we shall return to the use in Pacioli’s Treatise of two different models of ledger entries, a fact which is well know to scholars.

One of the passages that was more difficult to understand appears in Chapter 14 and refers to the convenience of recording in the Ledger, when posting the Journal entries, the credit accounts immediately after the debit accounts or, at least, as close as possible. Pacioli says, however, that even if it is not done so, it will not matter very much: “E nota che sempre quanta piu presso tu porrai mettere el creditore al suo debitore sera piu ligadro, avenga che posto dove si voglia, tanto tnonti. Ma per rispetto del milesimo, che ale volte se interpone fra una partita e laltra responde male, con fatiga non poca se ritrovano lor tempi . . . E pero sempre studia dassetar ditto creditore immediate a presso el suo debitore in la medema faciata o vero in la imediate sequente, non interponendovi fra luno e laltro altra partita.” Added to the real interpretation difficulties of this passage are those caused by the indiscriminate use made by Pacioli in the first part of his Treatise of the term partita to designate both an entry and an account. No wonder translators and scholars have faced serious interpretation problems. In my Spanish version, I have translated the passage as follows: “And note that the closer you place the account for the credit entry to the account for the debit entry, the better the accounts will be located, although it actually does not matter very much where the credit account is placed. But it could make a bad impression if an account corresponding to a different year is interposed between the debit and the credit account, as it may sometimes occur, apart from the difficulties that would arise in locating the accounts by their date . . . For this reason, always try to place the credit account immediately after the debit account, in the

28 It is possible that this apparent contradiction has something to do with a different treatment depending on whether the entry was the first one in the page or not, as Basil S. Yamey thinks. In fact, it seems that this was the practice in Venice in the fifteenth century.

same folio,29 or in the following one, without interposing any other account between both.”

In Chapter 15, Pacioli insists that accounts should be entered in the proper place (suo condecente luoco), without prejudice when two or three accounts may be recorded in the same folio, if there is sufficient place. In Chapter 28, he makes clear what is meant by proper place when explaining how accounts are carried forward to a new folio: “E questo medesimo modo observarai in tutte partite che havesse a reportare avanti, incatinandole al modo ditto e senca intervallo alcuno, pero che sempre le partite si vobliano ponere come nascano de luogo sito di e milesimo, acio nisun te possi caluniare,” i.e., “You will do the same with all the accounts you will have to carry forward to a new folio, linking them as explained, without leaving any blank between them and the previous ones, because accounts should always be placed in the proper place, following the same order

29 As can be observed, the term used by Pacioli is faciata, which is one more reason for having; translated it in a previous passage as double page or folio of the Ledger. This is what we have done in this case, taking for granted that Pacioli kept the debit and credit entries in the Ledger not in a single page, as it would also be possible, but on two facing pages.

30 Jager does not translate partita as account but as Posten, entry. This leads him to misinterpretations when referring, as in this passage, to Ledger entries. He himself realizes that he is not on firm ground and says in a footnote with respect to Pacioli’s remark that it will be better to place the credit account near the debit account: “P. hat, wie aus detn folgendem Satze hervorgeht, hier die Zeitfolge im Auge, welche sowohl im Soil als in Haben moglichst einzuhalten sei, was aber nur hbei Detaileintragung moglich ist,” i.e., “As it can be seen in the following sentence, P. refers to the chronological sequence that should be main tained whenever possible both on the debit and the credit sides. However, this is
only possible with loose entries.” In the second part of the passage, he omits any reference to faciata. Penndorfs version is not very different, although he does not make any remark and translates faciata as page in the second part.

Geijsbeek also interprets partita in this context as entry and, for the sake of consistency, translates faciata as line, thus making it even more difficult to understand the passage. In contrast, Crivelli, translates in this case faciata as facing, although this does not improve the understanding of the text. Brown and Johnston increase confusion even more, trying to complete Geijsbeek’s version in a logical way and translating the second part of the passage as follows: “Always try in the Journal to place the credit following the debit in the same line or in the line immediately following.” However, this text does not refer to the Journal but to the Ledger. Haulotte and Stevelinck also interpret partita as poste, entry, their version being thus substantially similar to the previous ones, but they translate faciata as page. Cardenas follows the general trend and under stands that partita means entry although, in accordance with his previous version, he translates faciata as sheet. Antinori also interprets partita as entry.

in which they were originated, by their day and by their year, so that nobody may calumniate you.”

Likewise, in Chapter 15, it is mentioned that Ledger entries referred to accounts that only concern the books’ owner requires less explanations than other accounts. On the contrary, in the case of entries on which account is to be rendered, all the required information should be recorded, although it will always be possible to find more details in the Journal. This differentiation of accounts that only concern the books’ owner, that is of “quelle che solo a te sapartenga.no,” such as merchandise expenses, household expenses, income and expenditure, unusual expenses, etc., is also found in Chapter 34 when explaining how to close the old Ledger and open the new one. Some authors have found in this differentiation of accounts and in the greater accounting accuracy to be applied in the case of accounts affecting third parties a supporting argument to the theory that the concept of account and even doubleentry bookkeeping developed from the need for rendering accounts. Pierre Jouanique, in particular, mentions these passages to draw the attention to the fact that Pacioli distinguished between two types of accounts: those on which account was to be rendered to somebody and those on which account was only to be rendered to oneself. Thus he concludes that “le compte est quelque chose dont on rend compte,” i.e., “the account is anything on which account is rendered” [Jouanique, 1987].

At the beginning of Chapter 17, Pacioli provides a few examples of banks or deposit entities which have not always been interpreted well by translators. The first entity mentioned is the Loan House of Venice which was sufficiently known and was correctly interpreted. However, he adds: “in firenga, el mote dele dote in genoa li lochi,” references which have generally not been well understood.31 In the first case, Pacioli refers to the Dowry Fund of Florence that has recently been studied in depth by Julius Kirshner and Anthony Molho.32 In the case of Genoa, our

31Jager, for instance, refers to the Institut fiir Aussteuer, Dowry Fund, of Genoa and “sonstige Officien und Bureaux,” other offices. However, Penndorf is well informed and explains in a footnote what were the Dowry Fund of Florence and the loca of Genoa. Geijsbeek, Crivelli, Brown and Johnston, Haulotte and Stevelinck and Antinori practically say the same as Jager. On the contrary, Cardenas refers correctly to the Monte delle Dote of Florence and the Luoghi of Genoa.
32 Julius Kirshner and Anthony Molho: “The Dowry Fund and the Marriage Market in Early Quattrocento Florence,” in The Journal of Modern History, vol.

author refers to the Casa or Officium Sancti Georgii, a wellknown municipal public bank, created in 1408, that was one of the first in Europe after the Taula de Canvis i Comun Diposits of Barcelona, established in 1401, and the Taula de Canvis i Comun Diposits of Valencia, created in 1407. The luoghi or loca were standard bonds whose face value was 100 liras. These bonds, which all bore the same interest rate, were introduced in 1407 as a result of the drastic reform of the Genoese municipal finance undertaken that year to reconvert and unify public debt and put an end to the countless debts and loans of all types incurred by the town council. The bonds’ owners grouped together, forming the aforementioned municipal bank [Felloni, 1991, p. 225246].

In this same chapter, Pacioli insists on the need, already pointed out in Chapter 3, to carefully keep the evidence of accounts held with banks and public offices due to the fact that these entities maintain business relations with so many people and are, moreover, accustomed to change accountants and clerks quite frequently. He ends up saying, after a short digression: “E pero fa che sia a casa e col capo a botega.” This sentence is surely difficult to understand, thus it has often been eluded or wrongly interpreted by translators. In my opinion, as I specified in my translation into Spanish, the sentence refers to the abovementioned evidence. Thus, the Spanish version is as follows: “Therefore, keep very carefully the evidence at home or under the care of the clerk in charge of your business.”

50, 1978, p. 403438. Later on, the subject was further studied in the work by Anthony Molho: “Investimenti nel Monte delle Doti di Firenze. Un’analisi sociale e geografica,” in Quaderni storici, vol. 61, 1986, p. 147170. See also the work by Julius Kirshner and Jacob Klerman on this same fund: “The Seven per Cent Fund of Renaissance Florence,” in Banchi pubblici, banchi privati e monti di pietal nell’Europa preindustriale. Amministrazione, tecniche operative e ruoli economici. Atti del Convegno, Genova, 16 ottobre 1990, nella sede delta Societa Ligure di Storia Patria, Genoa, 1991, p. 367396.

33 Jager, who translates scontro, receipt, warrant, as Rechnung, account, calculation, trying to find a meaning to the whole context, translates the last part of the passage as follows: “Sorge deshalb dafiir, dass Du die Aufmerksamkeit zu Hause und den Kopfin dem Laden behalst, wenn du mit solchen Leuten zu thun hast,” i.e., “Therefore, be careful to keep your attention at home and your head in the store when you have to deal with that kind of people.” Penndorf says something similar: “Sorge deshalb dafiir, dass Du darin zu Hause bist und mit solchen Leuten mit Bedacht handelst,” i.e., “Therefore, be careful to be at home and deal with these people with every caution.” Geijsbeek attributes the same meaning to this passage: “Therefore, be very careful when dealing with them,

Chapter 17 also contains a passage with another linguistic difficulty that made translators rack their brains. Referring to accounts kept with public offices, Pacioli says: “E cosi tirrai conto con li gabellari e datiari de robbe che tu vendi e compri, cavi e metti nele terre, etc., come si costuma fare in vinegia, che si tiene per li piu dela terra conto longo con lo officio dela messetaria.” The expressions “cavi e metti nele terre,” i.e., “bring in or take out of the country” or “unload or load,” “import or export” and “per li piu dela terra,” i.e., “in most of the country” have raised the greatest difficulties even to such an expert on Pacioli’s work as the historian of Italian accounting Carlo Antinori. I have given the following translation to this passage as I believe it may be the most correct: “You will do the same with the accounts you keep with tax collectors on things you sell and buy, or load and unload, as it is customary in Venice where most people hold an extensive account with the office of the Messetaria.”

and be observant at home and keep your head in the store.” Crivelli introduces significant changes: “Therefore if you keep an eye over them at home, and having a chief to look after them at the business premises they may perhaps carry out their work in good order.” Brown and Johnston give a mixed interpretation: “Therefore, deal as carefully with them as you would with at home, and have a chief watch your employees at the store.” Haulotte and Stevelinck provide a somewhat abridged version but always in the same line: “Vous devez avoir I’oeil et garder votre t&te dans vos operations avec eux,” i.e., “You have to keep an eye and your head in your operations with them.” Cardena’s translation is the freer of all: “Es por esto que, sea en tu casa o en tu bodega, tendrds que hacer las cosas con cuidado” i.e., “For this reason, you will have to do things very carefully both at home and in your store.” Antinori gives a similar version to the previous ones: “Per questa ragione tu devi fare molta attenzione e badare alia tua testa nelle tue operazioni con questi tali” i.e., “For this reason, you will have to be very careful and keep your head in operations with these people.

34 Jager translates the expression “cavi e mette nele terre” as “Aus dem Keller heraus nimmst oder in denselben hinein legst,” i.e., “Take out or put in the cellar.” However, he translates correctly “per li piu dela terra” as “die Meisten,” most. Penndorf interprets the expression in the same way. Geijsbeek believes the first expression refers to an agricultural activity: “Things that you grow, things that you plant.” However, the second expression is correctly translated. Crivelli, Brown and Johnston and Haulotte and Stevelinck follow the same line, which is also adopted by Carlo Antinori: “Nella stessa maniera tu curerai i tuoi conti con i gabellieri e i dazieri per la merci che tu acquisti e vendi, ricavi o semini nella terra como si usa a Venezia, dove si tengono conti importanti per i frutti della terra,” i.e., “In the same way, you shall keep your accounts with the gabellieri and dazieri of the merchandise you buy and sell, gather or plant in the ground, as it is customary in Venice, where important accounts are kept in relation to the fruit of the land.” Cardenas simply does a literal translation which is for this same reason more or less correct: ” . . . de lo que sacas y de lo que metes en la

A new difficulty arises also in this chapter in relation to purchases and sales intermediated by Messetaria brokers. It is said that the name of the broker who has intervened in the operation must be indicated in the entry and, moreover, “anche la mare in su che fa, doe el libro dove da in nota li mercati al ditto officio che cosi lo chiamano in venetia,” i.e., “also the master book in which the operation is recorded, as this book is called in Venice.” Although the second part of the sentence clarifies rather well the meaning of the expression, the words “e anche la mare in su che fa” have made life difficult for more than one translator.

Another complicated passage appears in Chapter 18 where Pacioli explains as follows how to enter payments or collections of purchases and sales carried out through the Loan House: “E similmente se piu a la giomata ne comprasse, che molti se ne vendano, per te o per altri, come sa chi realto usa, nota ben in chi sono scritti e luoghi.” There is a certain confusion among translators with respect to the interpretation of this passage. I have translated it myself in the following way: “Similarly, if you buy one day more than you sell, since much is sold there, to you or to others, as anybody accustomed to doing business on the tierra, etc., como se acostumbra hacer en Venecia, en donde se tiene que llevar, por la mayoria de la tierra, cuentas extensas . . .,” i.e., “… of what you take out or put in the land, etc., as it is customary in Venice, where extensive accounts are to be kept for most of the land … “.

35Jager translates la mare as das Meer, the sea. However he perceives the correct meaning of the expression when he translates literally. “Auch das Meer ist zu notieren beziiglich dessen er handelt, namlich das Buch, mittelst dessen er die Kdufe besagtem Bureau vorweist,” i.e., “You must also note the sea where business is recorded, that is the book through which purchases are communicated to the mentioned office.” As usual, Penndorf is better informed and explains in a footnote: “Mare bedeutet hier nicht Meer, sondern Matrize, Stammverzeichnis oder einfach Buch, wie auch das Haupthuch der Monteverwaltung in Venedig Mare hiess,” i.e., “Mare does not mean here sea but master book, original record or simply book, the same as the Ledger of the Dowry Fund of Venice was also called Mare.” Although he correctly interprets the general meaning of the passage, Geijsbeek gets a little mixed up and says that it is also necessary to indicate the special mark — possibly for mare — made by the intermediary in the book in which he records the operations negotiated on behalf of the Messetaria and which is called in Venice “Chiamans.” It is not possible to ascertain where Geijsbeek found such a name that can only be a transposition of the verbal form chiamano. Brown and Johnston reproduce these two mistakes in their translation. In contrast, Crivclli only refers to the mark, the same as Haulotte and Stevelinck. Cardenas uses correctly the term “libro matriz” master book, to translate la mare and, in the same line, Antinori calls it “la madre.”

Rialto knows very well, check carefully to whom the monies are credited and where.” Therefore, in my opinion, this sentence means that if, one day, you must pay more than you collect, because you have made more purchases than sales, you will credit the balance to the sellers’ account through your bank, i.e., the Loan House, in which case you will have to check carefully that the money is credited to the correct account and to the correct office of the Loan House (as this House had offices in the various districts of the town).36
36Jager translates this passage as follows: “Auf gleiche Weise verfahrst Du, wenn Du mehr an einem Tag davon kaufst, denn es wird Vieles verkauft sowohl fur Dich als fiir Andere, wie Derjenige weiss, der Rialto oft besucht. Merke Dir daher wohl den Namen, aufwelchen die Waare eingeschrieben ist, und den Ort, wo sie liegt,” i.e., “You will do the same, if one day you buy more because much is sold, both to you and to others, as anyone who does business on the Rialto knows. And carefully note to whom the merchandise is consigned and the place where it is.” This text does not seem to make much sense, the more as these are banking operations with the Loan House. The translation Penndorfs makes even less sense: in the following sentence, where Pacioli refers to the reimbursement of funds deposited in the account, he says: “Beim Ahheben der Zinsen i.e., “when collecting interest,” whereas this is not the subject at all. Geijbeeks even converts purchases into sales, saying: “Likewise, for the amount of the daily sales for many are the sales made for you or for others, as those people know who are familiar with the Rialto. Be careful to put down the name of the party that buys and his place of business.” Crivelli does not understand the text either, although he gets nearer to the correct meaning in some aspects: “And similarly, if the daily purchases are more than your sale or sales for other people, carefully note to whom the goods are sold, and their business addresses, as do those who know, and who are familiar with the customs of the Rialto.” Brown and Johnston provide a mixed interpretation based on the two former ones. Haulotte and Stevelinck do not make any progress in their translation into French: “Si vous achetez davantage de marchandises en un jour que vous ne vendez pour vous et pur autres, comme le savent ceux qui sont familiarises avec le Rialto, vous notez soigneusement a qui les marchandises ont ete vendues et d’oit Us sont,” i.e., “If one day you buy more goods than you sell, for yourself or others, as those who are familiar with the Rialto know, carefully note to whom the goods were sold and where they are.” Cardenas does not cast any light in his translation: “Y similarmente, si en el dia tus compras son mayores que tus ventas, por ti mismo o por otro, como sabes que se usa en Rialto; anota bien el nombre de a quien fueron inscritas, los lugares,” i.e., “Likewise, if one day your purchases are greater than your sales, for yourself or for others, as you know it is customary on the Rialto, carefully note to whom they were recorded and the place.” Antinori follows the same line as the previous translators, although he tries to give a more consistent version: “Se tu acquisti dapprima della tnerce in un giorno in cui non vendi ne per te ne per gli altri, come sanno coloro che usano frequentemente il mercalo di Rialto, annota bene da chi le merci sono state vendute e dove si trovano,” i.e., “If you buy goods one day in which you do not sell, neither for yourself nor for others, as those who are familiar with the Rialto

In this same chapter, the following passage has also given rise to numerous doubts in connection with the permit to take the purchased goods away on payment of duties to the Messetaria: “E pero poi a tal compratori li e concesso di cavare tanto di quella mercantia per quanto a pagato la messetaria fora de la terra in loro bolette a la tavola de luscita o per mare o per terra che la vogliono cavare ala giornata. E pero convengano li mercanti tenere ben conto con lo ditto officio, ado sempre sapino quanto possino cavare, perche non si lassano cavar per piu che si comprino se di novo non paghino la messetaria de contanti.” As can be seen, this passage is obscure and has, therefore, originated different interpretations among translators. My own translation is as follows: “Thus, buyers are allowed to take out of the country as many goods as they have paid for to the Messetaria, if they show the corresponding receipt at the exit counter, and they can take them out by land or sea, as many as they want to take out in the day. Therefore, merchants should keep a careful account with this office, so as to know at any moment how much merchandise they can take out, because they are not allowed to take out more than they have bought, unless they pay the corresponding duties to the Messetaria.”

market know, carefully note who sold the goods and where they are.” The same as it occurred with Jager’s interpretation, none of these versions takes into account the context in which it appears, that is the recording of the operations carried out through the account held by the merchant with its bank; neither do they interpret correctly the banking term “scritti,” i.e., “credited.”

37 Jager’s translation of this passage is full of question marks because it did not make any sense even to him. In effect, he says: “Aus diesem Grunde darfder Kdufer so viel von detn Waarenpreise abziehen, als die Messelarier ausserhalb der Erde (Venedigs?) bezjMt haben. (?) Der Kdufer darf desshalb diejenigen Waaren abfuhren, fiir welche die Messetarier nach ihren Frachtbriefen ausserhalb der Erde in ihren Laden am Tische des Ausganges bezahlt haben, sei es zu Wasser oder zu Lande, weil man an diesem Tage es aus den Kellern (Magazinen) ziehen will. Desswegen sollen die Kaufleute ihre Rechnung mil besagtern Bureau gut fiihren, datnit sie immer wissen, wie man Waaren herausziehen kann, denn man Idsst nicht mehr abfuhren, als das (im Verhdltnis zu dem Betrage des Erlegten), wenn man die Messetarier nicht wieder mit baarem geld bezahlt, etc. (?).” It is a laborious and obscure text, full of inconsistencies and ambiguities that could be more or less translated as follows: “For this reason, the buyer can deduct from the price of the merchandise the amount paid by Messetaria officials out of the land (Venice?) (?). The buyer can thus withdraw the goods that Messetaria officials, in accordance with their bills of lading, have paid out of the land at their counters of the exit table, both by land and sea, because they want to take them out of the warehouses on that day. For this reason, merchants must keep well their accounts with the mentioned office, so that they may always know how to

The title of Chapter 19 also contains an expression that has caused difficulties to translators: “Commo se debia ordinare el pagamento che havesse a fare per ditta e banco d scritta ne li tuoi libri principali,” i.e., “How to record in your main books payments made by draft or by crediting a bank account.” In Chapter 9, which describes the various ways of paying the purchase of a merchandise, we already find the term “asegnatione de ditta,” that should be translated, in my opinion, as draft or payment order against a bank, as mentioned before. This time, Pacioli makes a difference between payment by ditta and payment by bank transfer from one account to another or scritta di banco. In effect, the concept banco d scritta used by Pacioli means deposit bank and generally refers to banks which took deposits from their clients to whom they provided custody and payment services through cash payments for their account

take goods out, since they are not allowed to take more out (in proportion to the amount paid), unless they pay again to Messetaria officials in cash, etc. (?).” In contrast, Penndorfs translation is totally clear and is generally in agreement with my own, although he calls the tax or brokerage paid to the Messetaria Umsatzsteuer, i.e., turnover or sales tax, which is maybe specifying too much. Geijsbeek gives a somewhat different version in which there are a certain lack of foundation and some inconsistencies: “In accordance with this, the buyer will be allowed to take out of the official warehouses merchandise in proportion to the brokerage paid and according to their books kept at the shipping counter, whether it came by land or sea. Therefore, the merchants should keep a careful account with the said office so that they know how much merchandise they can take out. They are not allowed to take out more than they have bought unless they have paid the extra brokerage.” Crivelli gives a similar version in which he also mentions the warehouses which appear in Geijsbeek’s translation. Brown and Johnston do the same. Haulotte and Stevelinck provide an interpretation which is basically correct but omit the difficult and controversial parts, saying only that: “L’acheleur est autorise a disposer de marchandises, en proportion des droits payes et conforme’ment aux livres tenues, venues par terre ou par mer. Partant, les marchands doivent tenir un soigneux compte avec ledit Office afin de savoir de combien de marchandises Us peuvent disposer parce que, comme il est aise a cotnprendre, its ne peuvent disposer de plus de marchandises achete’es sans en avoir pays les droits an Messetaria,” i.e., “The buyer is allowed to withdraw the goods in proportion to the duties paid and in accordance with the books, whether they have come by land or sea. Therefore, merchants must keep a careful account with the mentioned office in order to know how many goods they can withdraw because, as it is easy to understand, they cannot withdraw more goods than they have bought without paying the corresponding duties to the Messetaria.” As can be seen, any references to taking out of the country, exit counter, as many as they wish in the day, etc., have disappeared in this version. Cardenas does not make any new contribution and also avoids controversial points. Antinori also provides a correct interpretation, without going into complicated details, in line with the translation of Haulotte and Stevelinck.

{ditto) and noncash payments by transferring the amounts from one current account to another (scritta di banco). In the case under review, the expression banco di scritta used by Pacioli refers not so much to the banks that performed this type of operations as to the operation itself of crediting an account through a transfer from another account. As already mentioned, this operation was actually called, as Pacioli does in other parts of the Treatise, “scritta di banco,” since the verb scrivere had, in this context, the meaning of crediting an account.38 The fact that a number of translators did not exactly know this banking idiom has created some difficulties to them in various parts of the Treatise — among others, the recently mentioned passage on crediting sellers’ accounts if daily purchases exceeded sales on the Rialto market.

38Federigo Melis calls this type of crediting by transfer to a bank account giroconto operations. See his works “Note di storia della banca pisana nel Trecento” and “La grandc conquista trecentesca del ‘credito di esercizio’ e la tipologia dei suoi strumenti fino al XVI secolo,” both reproduced in Federigo Melis: La banca pisana e le origini della banca modema, Florence, 1987, p. 55293 and 307324, respectively. See also Florence Edler: Glossary of Medieval Terms of Business. Italian Series 12001600, Cambridge, Mass., The Medieval Academy of America, 1934, p. 40 and 265.

39 With respect to the title of Chapter 19, maintaining the line followed in chapter 9, Jager translates the part under review simply as: “Wie man die Zahlung einzurichten hat, welche man durch eine Firma oder Bank zu machen hat. . . ,” i.e., “How payments are to be made through a trading house or through a bank…”. Penndorf also translates this part in accordance with Chapter 9 but he corrects the inaccurate use of the word Burgschaft: “Wie Du die Zahlung, die Du durch Bankschein und Girobank zu machen hast. . .,” i.e., “How to effect payments by draft or payment order against a bank or through a deposit bank.” The only objection that could be made is that he provides a literal translation of Pacioli’s words and does not translate the second form of payment as “bank transfer or by crediting a bank account.” Geijsbeek also interprets rather well the sentence, though he still considers ditto, as a bill of exchange and not as a check against a current account, which is what it would be in modern terms. In effect, he translates: “The payments that we have to make either by draft or through the bank.” In the text, he stresses the identity between draft and bill of exchange. Crivelli, Brown and Johnston and Haulotte and Stevelinck adopt the same translation. Cardenas leaves the terms in Italian, without translating them, although he tries to explain them — rather unsuccessfully — in two notes. To him, ditta is a payment order issued by a trading firm in favor of a similar company. When referring to banco di scritta, though his explanation starts well, at the end it goes wrong. He says: “Refie’rese a una prdctica reconocida en Venecia, la cual permitia a un Banco privado operar transferencias o pagos por cuenta de sus clientes: un antecedente, al parecer, del ‘cheque’ bancario,” i.e., “This was a customary practice in Venice which allowed a private bank to make transfers or payments on the account of its clients:

There is a passage in this same Chapter 19 whose literal translation does not raise difficulties but whose accounting and financial meaning escapes me. It reads as follows:”Ma quando hai a far pagamento a parte banco e ditta, fa che prima consegni la ditta, e poi per resto scrivi in banco per piu sigurta. Unde ancora questa cautella susa per molti, e bene, quando ben pagassero a contanti de far per resto in bancho.” My translation is: “When you have to make a payment part through the bank and part by draft, deliver first the draft and then, for the rest, let the bank credit the payee’s account, as a safety measure; when they have to pay part in cash and part through the bank to complete payment, many people take the same precaution, and they do well: so they enter the cash payment first and then the rest through the bank.”

apparently an antecedent of the bank check.” Antinori also assimilates ditta to bill of exchange, as he did in Chapter 9.

40 In his interpretation, Jager goes beyond the purely accounting context and says in this respect: “Wenn Du aber eine Zahlung theilweise durch die Bank und theilweise durch eine Firma zu machen hast, so sorge, dass die Firma vorher bezahle, dann hast Du nur den Rest durch die Bank umschreiben (scrivi) zu lassen, was zu grosserer Sicherheit dient,” i.e., “When you have to make a payment part through the bank and part through a company, make sure that the company pays first because, in this way, you will only have to transfer the rest through the bank, which will be safer.” Penndorf also goes beyond the accounting context but he translates Pacioli’s words correctly and proves that he has perfectly understood the meaning of the banking instruments used, although he does not say a word on why Pacioli thinks this is the safest procedure. He translates the passage as follows: “Wenn Du aber eine Zahlung teils durch die Bank und teils durch Bankschein zu machen hast, so ha’ndige zuerst den Bankschein aus und schreibe dann den Rest durch die Bank zur grosseren Sicherheit um,” i.e., “When you have to make a payment part through the bank and part by draft or bank payment order, first deliver the draft and then transfer the rest through the bank, as a safety measure.” Geijsbeek’s translation is practically the same, except that he replaces the correct term of bank piayment order by bill of exchange: “But when you make a payment part through the bank and part by bill of exchange, deliver first the bill of exchange and then settle through the bank, which is safer.” Crivelli and Brown and Johnston use practically the same terms, replacing bill of exchange by draft. Haulotte and Stevelinck adopt the same translation as Geijsbeek, also using the expression bill of exchange: “Quand vous avez a faire un paiement, partie par Banque et partie par traite, delivrez la traite la premiere et ensuite reglez par Banque, ce qui est le plus sur.” Antinori does the same: “Quando devi fare un pagamento, parte per banca e parte per tratta, regola per prima la tratta e dopo paga per banca, perche e piu sicuro,” although he does not use the word “deliver” with respect to payment by bill. Cardenas’ translation is somewhat obscure: “Mas cuando tengas que hacer pagos parte por el banco y parte por giro comerdal, te conviene primero entregar el giro y despuis por el resto girar al banco, para mas seguridad,” i.e., “When you must

The same occurs to me with another expression in the same chapter which explains how to record goods sold to others, “facendoli debitori (to buyers) e creditrici le tue rohbe, e debitrici la cassa se ti da contanti, e debitrici le ditte se te le consegna in pagamento, e creditore el banco se tel da.” I decided to interpret this passage as follows: “you will debit to them (the buyers) the amount of the goods, crediting the merchandise account, or you will debit the Cash account, if they pay you cash, or the draft account, if they pay you with a draft, and you will subsequently credit the account when the bank settles the draft.” This translation has been adopted by several translators, except that they refer to bills of exchange instead of drafts or bank payment orders. However, I am afraid it is not correct, because Pacioli says: “and credit the bank if it gives it to you” — an expression which does not seem to make sense. For this reason, I am inclined to think that Pacioli or the printer made a mistake and put down “creditore el banco,” instead of “debitore el banco,” i.e., “debit the bank.” In this case, the expression would make sense because it would refer to collection through the bank, that is, that the bank would credit our account (i.e., the sellers’ account) and would, moreover, complete the various ways of collection considered.

effect payments part through the bank and part by commercial draft, you should first deliver the draft and then draw the rest on the bank, as a safety measure.”
41 Following the idea that ditta means company or trading house, Jager gives a completely different translation which does not make any sense either: “Indent Du die Kaufer zu Schuldnern und Heine Waaren zu Gldubigern machst, ferner die Kasse zur Schuldnerin, wenn man Dir baares Geld gibt, dessgleichen die Firma zu Schuldnerin, wenn sie die Bezahlung leisten soil und die Bank zu Glaubigerin, wenn sie bezahlt,” i.e., “Debiting buyers and crediting goods or debiting the Cash if cash money is delivered to you, or in the same way debiting the company if payment is made by same and crediting the bank, if payment by the latter.” Penndorf s translation is more correct and tries to be more consistent, although not quite successfully: “Indent Du die Kaufer zu Schuldnern und Deine Waren zu Gldubigern machst, femer die Kasse zum Schuldner, wenn man Dir bares Geld gibt, desgleichen die Bankscheine zu Schuldner, wenn man sie Dir in Zahlung gibt, und die Bank zum Gldubiger, wenn sie Dir solche gibt.” The first part of the translation is identical to Jager’s . Differences appear when referring to ditta: “or also debiting drafts if they are given to you in payment, and crediting the bank if they are delivered to you by the latter.” Geijsbeek translates the passage the same as Antinori and myself: “And you shall charge bills of exchange if you get a bill of exchange in payment, and credit the latter when the bank pays the exchange,” except that I do not use the expression bill of exchange. As usual, Crivelli, Brown and Johnston and Haulotte and Stevelinck follow Geijsbeek’s

A similar case appears in Chapter 23. Here again, literal translation does not raise any difficulty but there seems to be an accounting contradiction. Pacioli explains how to record the operations of a shop which has been entrusted to a clerk or that we carry out by ourselves. In the latter case, he assumes that all our business is done through that shop and that we do not carry out any other type of operations: “E metiamo eke compri e trafichi tutto per la ditta botega e non havi altro maneggio, alora formarai li libri commo e ditto, e di do che vendi e compri farai creditori chi te da le robbe per tanto tempo se compri a tempo e creditrici la cassa se compri a contanti, e debitrici la botega.” The translation of this passage is clearly: “Let us assume that all you buy and sell is channelled through the shop in question, so that you have no other type of operations. In this case, you will keep the books as I explained in general. You will credit the amount of what you sell and buy to the person who sells you the merchandise on credit, if you buy it on credit, or the Cash account, if you pay cash, debiting the amount to the shop.” The contradiction lies in the fact that, if all the business is run through the shop, there is no point in keeping a shop account separating business done through the shop from the rest of our operations. In this example, it seems that it would be reasonable to debit the account of goods purchased. However, no observation in this respect appears in any of the translations consulted.

In Chapter 24, there is an expression that not all translators have translated with the same accuracy. Pacioli says: “E se tu li scrivessi ad altri farai debitore quel tale e creditore detto bancho o patroni di quel tanto noiando el perche.” A little below, he provides the example of the entry to be made: “Per martino del tale al ditto ut supra (the banker Girolimo Lipamani) per ducati tanti, etc., li scrissi per parte o per resto o a bon conto o per impresto etc. in questo di.” The correct translation of these texts could be: “And if you make a transfer, that is, if you order to credit an amount to somebody’s account, you will debit to that person and credit to the bank or its owner the amount in ques
interpretation. Cardenas does not really understand the meaning: “Por todo lo que tu vendas a otros, deberds hacerlas deudoras y acreedoras a tus mercancias, y deudora a la Caja, si te dan efectivo; deudoras a las dichas (mercancias) si te las entregan algunos como pago, y acreedor al banco, si el te paga,” i.e., “For all you sell to others, you shall debit them and credit your goods, and debit the Cash, if they pay you cash; you shall debit same (the goods) if they are delivered to you in payment, and credit the bank, if the latter pays you” As it is clear, he thought ditta meant ditto in this case.

tion, indicating the reason.” And: “From Martino soandso to the abovementioned, for as many ducats as I ordered to credit to his account in part or in balance or on account or as a loan on that day.” However, some translators do not mention the fact that payment is made precisely through a bank transfer from one account to another.42 As a result, the payment procedure used is not specified, when the point in this explanation is just the specification of the accounting employed for this form of payment. As we have already seen before, Pacioli uses a draft account when collections are made through such instruments. Nevertheless, some translators interpret, in my opinion mistakenly, that in this case, payment is made through a cash payment order, surely because they have not understood correctly the meaning of the term scrivessi, you will credit. However, in German there is still an accounting and banking idiom which derives directly from this expression or, at least, has the same root: gutschreiben, i.e., to credit. Another clear example of this type of recording, this time from the standpoint of the bank that effects the transfer between the accounts of two of its clients, appears in the same chapter when the monk of Sansepolcro explains the entries to be made by bankers.

42 Jager translates the mentioned passage as follows without understanding what it is about: “Wenn Du es fur die Rechnung eines Anderen thust, so wirst Du jenen Herrn Zum Schuldner und die Bank zur Glaubigerin machen,” i.e., “If you act on behalf of another person, you will debit him and credit the bank.” On the contrary, Penndorf perfectly understands the operation and translates it quite accurately: “Wenn Du es anderen iiberweist, so wirst Du jene anderen zum Schuldner und die Bank oder ihren Inhaber fur diesen Betrag zum Glaubiger machen,” i.e., “If you transfer it (the money) to others, you will debit them and credit the bank or its owner for this amount.” Geijsbeek does not understand the passage very well and believes it is a cash payment order and not the crediting of a transfer to an account, reason for which he says: “And if you should give an order on the bank for somebody else, you shall charge this party and credit the bank or owners of the bank for that much.” He translates accordingly the entry given as an example to illustrate this operation: “Per Martino on such and such a day // A ditto for ditto for cash, etc., for so many ducats, for which I gave an order.” Both Crivelli and Brown and Johnston follow Geijsbeek’s interpretation and mention expressly the payment order without realizing that the operation described by Pacioli is a transfer from a bank account to another. Carlo Antinori seems not to understand the operation either. Haulotte and Stevelinck refer in the text to an order given to the bank to pay to somebody but they translate correctly the example: “Par Martino de tel et tel II A Ditto ciavant pour tant de ducats que j’ai fait transferer,” i.e., “From Martino Soandso // To ditto above for so many ducats as I ordered to transfer.” Cardenas translates the passage correctly, understanding that it is a transfer.

Another controversial point arises in Chapter 24 from Pacioli’s explanation of the intermediation services provided by bankers to the parties to whom they offer their work, effort, time, testimony, premises and even paper and ink: “E vieni in questo atto essere persona meggana e communa, commo testimonio e factore de le parti a tuo inchiostro, carta, fitto, fatiga e tempo.” Precisely due to these intermediation services, Pacioli thinks that: “Di qua si cava la honesta provisione nel cambio essere sempre Ucita quando mai non vi corrisse pericolo de viaggio altre remesse in mano de terge persone.” This passage can be interpreted as follows: “It can thus be concluded that the honest commission charged on bills of exchange is always licit, although there are no travel risks such as when money is brought from abroad by third parties.” This is the interpretation given by most translators. However, it can also be considered, as do other translators among whom I include myself, that what the sentence really means is: “It can thus be concluded that the honest commission charged on bills of exchange is always licit, the more as there are no travel risks as when money is brought from abroad by third parties.”43 There is not much difference really but the shade of meaning is not quite the same.

43Carlo Antinori attributes the same meaning to the passage: “Per il tuo inchiostro, carta, fitto, fatica e tempo tu prendi la tua onesta provvigione. Questa e sempre permessa specie quando la tratta non corre il rischio di un viaggio o quando la moneta deve essere trasportata da una terza persona.” The other translators consulted opt, more or less extensively or correctly, for the opposite version. For instance, Jager translates the passage as follows: “Fur Deine Tinte, Dein Papier, Deinen Zins, Deine Miihe und Zeit nimmst Du eine hesch.eide.ne Provision in Anspruch, welche immer erlaubt ist auch wenn das Geld beim Wechsel nicht die Gefahr der Reise unterworfen ist, welche bei den cambi reali (den wirklichen Tauschen) auftritt,” i.e., “For your ink, paper, interest, effort and time you will receive a reasonable commission which is always allowed, although with bills of exchange there are no travel risks as with cambi reali!’ Penndorf also adopts this version: “Fur Deine Tinte, Papier, Miete, Miihe und Zeit ziehst Du eine bescheidene Provision ab, die beim Wechsel immer erlaubt ist, wenn auch heine Gefahr der Reise oder andere Ubergabe in die Hand dritter Personen besteht usw.,” i.e., “For your ink, paper, rent, effort and time you will receive a reasonable commission which is always allowed on bills of exchange, although there is no travel risc nor the risk to deliver money to third parties.” Geijsbeek, Crivelli, Brown and Johnston, as well as Haulotte and Stevelinck follow the same line. In contrast, Cardenas provides another interpretation: “Puede ser que en estos casos exista una persona intermediaria como testigo y como empleado de una de las dos partes, que saca su comision, siempre que sea licito, cuando no hubiera peligro de traslado o de envios por media de terceras personas . . . como en los cambios de lugar o estado,” i.e., “In these cases, there may be an intermediary to act as a

In Chapter 25, Pacioli indicates the name of an account that has caused perplexity to more than a few scholars. This account had already been mentioned, without any explanation, at the beginning of Chapter 22 among expense accounts. The title of Chapter 25 says: “De unaltra partita che a le volte se costuma nel quaderno tenere detta entrata e uscita e a le volte se ne fa libro particulare; e per che,” i.e., “Of another account that is sometimes kept in the Ledger and is called income and expenditure, although it is other times kept in a special book, and why.” However, the text of the chapter, which is very short, does not answer the expectations raised by the title. The chapter actually begins as follows: “Sonno alcuni che nel lor libri usano tenere una partita detta entrata e uscita in la qual pongano cose straordinarie o altre commo a la fantasia pare,” i.e., “Some usually keep in their books an account called income and expenditure in which they record unusual items or whatever they may imagine.” The following sentence explains what those items may be: “Altri ne tirra una d spese straordinarie i simili mettano commo in quella dintrata isita presenti che li foser fatti, verbi gratia, e cosi, secondo che ricevano e danno, e tengano conto in dare e havere, e poi a la fine con laltre le saldanno in pro e danno e cavedale, commo intenderai nel bilancio.” The translation of this passage can be: “Others keep an unusual expense account in which they record, for instance, any presents received, the same as they do in the income and expenditure account. As they receive and give, they keep the account by recording the debit and credit entries. At the end, they close it, together with the others, by transferring the balance to the profit and loss account and to the capital account, as you shall see when we come to the balance procedure.” To specify further the nature of the items recorded in these accounts, Pacioli adds: “Ma in vero quella detta di sopra (in Chapter 22), spese di casa, per tutte e bastante, se non chi volesse per sua curiosita tener conto da per se fin a un portale de strenga che to porria fare, ma a che fine,” i.e., “Although the truth is that, the above mentioned household expense account will be sufficient, except for those who wish to keep a specific account even for a buckle or pin; and if you wish so, you can do it, but for what purpose?

witness and employee of one of the two parties, who receives a commission, whenever this is licit, when there is no risk of remittances through third parties … as in changes of place or condition.”

The inclusion of the entrata e uscita account in the group of expense accounts is clearly confirmed by the fact that it also appears among expense accounts in Chapter 22, as well as in the following passage of Chapter 34 that was already mentioned in another context: “Ma quelle partite che non volesse portare in ditto quaderno A, che porrienno essere quelle che solo a te sapartengano e non se obligato a segnarne conto ad alcuno, come son spesi de mercantia, spesi de casa, intrata isita e tutte spese straordinarie, fitti, pescioni, feudi o livelli, etc.” which means: “The accounts that you do not have to carry to the mentioned Ledger A, as may be those that only concern you and on which you do not have to render account to anybody, as merchandise expenses, household expenses, income and expenditure and all unusual expenses, rents, pensions, bestowals, taxes, etc.” On the other hand, this passage of Chapter 34 is the only place in all the Treatise, apart from Chapters 22 and 25, which mentions the account of entrata e uscita or intrata isita, as it is called in this and in a few other occasions, a name which is in any case surprising for an expense account, as it literally means in English entrance and exit. At the end of Chapter 25 in which this account is described, appears an observation which is even stranger considering the nature of this account in Pacioli’s mind: “Altri luoghi costuma de lintrata e uscita tenere un livro a sua posta; e poi quello saldano a tempo del bilancio nel ultimo autentico insiemi con le altre facende,” i.e., “In other places, they keep a book specifically for the income and expenditure account and they close it at the time of the balance by carrying its balance to the main book, together with that of the other operations.” This seems really disproportionate in relation to the little importance of a sundry and atypical expense account.

In view of these apparent inconsistencies, it is not surprising that Pierre Jouanique has recently related this entrata e uscita account to the balance de sortie and balance d’entree used by Mathieu de La Porte at the end of the financial year to close the old Ledger and open the new one. In fact, these closing and opening balance accounts were used for this purpose with a similar name in many countries, including Spain where, as I explained a few years ago [HernandezEsteve, 1989, p. 62], Ledger number 67 of the Taula de Canvi of Valencia was opened on 1 June, 1585, with an entry appearing directly in this book, without being recorded first in the Journal, under the heading “Entrada del Present Libre,” i.e., “Opening balance of this book,”

as contraentry of the other accounts. Similarly, it was closed on 31 May, 1586, with the account “Balans y Eixida del Present Libre,” i.e., “Closing balance of this book.” Therefore, it is quite possible that the account mentioned by Pacioli was used in the same way in some of the places referred to, and that Pacioli himself was aware of it, as assumed by Jouanique, yet the fact is that the monk of Sansepolcro does not seem to relate in any way the entrata e uscita account to the closing and opening procedure.44 In his Treatise, strange as it may be, he merely attributes to this account the function of recording sundry and atypical entries and expenses.

44 This is also the opinion expressed by Yannick Lemarchand in his comment to my paper. On the other hand, he adds that it would not be easy to understand that a closing and opening account would be included among the accounts which are to be closed by transferring their balance to the profit and loss account, since the balance of the latter must also be transferred, in turn, to the capital account. Moreover, if the entrata e uscita account were really a closing and opening account, Pacioli would not have included it among the ac
counts which concern exclusively the book’s owner, because the closing and opening account is precisely the one that gathers the balances of all accounts belonging to third parties

45 Jager translates the heading of this account as “Einnahme und Ausgabe,” i.e., “Income and Expenditure” but he explains in a footnote: “Hiermit ist nichtder CassaConto gemeint, sondern ein Conto fur ausserordentliche Spesen, wiediess aus dem Folgendem hervorgeht,” i.e., “In this case, it is not the Cash account but a nonrecurrent expense account, as it appears from what comes next.” When it is mentioned that in other places it is customary to keep a special book for this account, Jager explains: “Hier deutet P. schon an, dass es hesser sei, die Spesen in Hilfsbiichern zu notiren und monatlich, summarisch auf die betreffenden Conti in iibertragevi, welche aber nicht in Spesen, sondern in
WaarenConti zu bestehen haben, abgesehen von dem Conto fur Handlungs unkosten und dem CassaConto” i.e., “P. surely want to mean here that it is better to record expenses in subsidiary books and post them each month in an abridged form to the relevant accounts, which must not be expense accounts but merchandise accounts, leaving aside the overhead expense account and the Cash account.” However, as we have seen, Pacioli is very laconic in this respect.

It does not seem that he wishes to say all these things and less that the balance of the entrata e uscita account should be posted every month to another account. Penndorf uses the same terms as Jager to translate the heading of the account but without making any comment. Geijsbeek translates this heading as “Income and Expense” which has the same meaning as the expression used by the German translators. Crivelli calls it “Income and Expenditure” and Brown and Johnson “Income and Expense.” All of them are, thus, in the same line, the
same as Haulotte and Stevelinck who call the account “Revenus et Depenses.” It should be recalled that Jouanique, in a completely different line, thinks that this
expression is to be translated as entree et sortie, which is equivalent to “Balanced’entree et de sortie,” i.e., “opening and closing balance.” Cardenas leaves the

In saying in Chapter 27 that the profit and loss account need not appear in the Journal because it originated in the Ledger as a result of the closing of accounts that have given some profit or loss and should, therefore, appear only in this book, Pacioli introduces another passage that has raised many doubts. He says: “E questa partita (the profit and loss account) poi ancora lei si converra saldare in quella del cavedale, la quale e ultima de tutti li quaderni e, per consequente, receptaculo de tutte le altre.” These words do not seem too difficult to translate literally. My own version reads as follows: “Then, you will balance this account with the Capital account which is the last one to be closed in the entire Ledger, thus being the receptacle of all the others.” This passage has clearly led some translators to think that Pacioli recommended to make closing and opening entries as contraentries to the Capital account, as explained by some scholars.46 However, in Chapter 34 and also in the summary

term untranslated at the beginning of Chapter 25 but explains in a note: “Tirmino que hemos traducido como: Entradas y salidas, o sus equivalentes,” i.e., “Term that we have translated as Income and expenditure, or equivalent.” In the last passage of the chapter, referring to what is customary in other places, he precisely says: “En otros lugares se acostumbra tener un libra separado para registrar los ingresos y los gaslos a voluntad,” i.e., “In other places, it is customary to keep a separate book to record income and expenditure at will.” Thus, he expressly and undoubtedly agrees with those who think that this account included, as Pacioli said, atypical income and expenditure. Antinori uses the same words as Pacioli in his translation, i.e., entrata e uscita.

46 With respect to this subject, Carlo Antinori says for instance that “Per aprire o chiudere i conti non si usano i conti Bilancio di Apertura e Bilancio di Chiusura, n£ si usa contraporre tutti i conti accesi alle attivita ai conti accesi alle passivita e al capitate netto, ma si usa il conto CAPITALE che serve di contropartita per aprire o chiudere i conti accesi alle attivita e alle passivita” (“II Trattato dalla ‘Summa’ del Paciolo. A cura di Carlo Antinori,” in Summit. Gli speciali di Summa. Supplemento al n. 40 di Summa, November 1990, p. 7). Jager translates this passage as follows: “Welcher (the Capital account) der letzte aller Hefte und daher das receptaculum aller anderen Posten ist,” i.e., “Which is the last one of all the books and, thus, the receptacle of all the other entries.” Penndorf gives a more accurate translation: “Welches das letzte in alien Hauptbiichem und folglich der Zufluchtsort aller anderen Konten ist,” i.e., “Which is the last one of all the Ledgers and, thus, the shelter of all other accounts.” Geijsbeek gives a similar translation, though he uses the word receptacle instead of shelter, the same as Crivelli and Brown and Johnston. Haulotte and Stevelinck want to be more accurate and say: “Qui reste toujours le dernier de tous ouvert au Grand Livre, et qui est le receptacle de tous les autres comptes,” i.e., “Which is always the last one to remain open in the Ledger and, thus, the receptacle of all the other accounts.” Cardenas also wishes to provide a more accurate translation and replaces receptacle by summary: “La cual es la ultima de todos los libros Mayores offered in Chapter 36, it is clearly specified that the accounts of the old Ledger must be balanced and closed separately, one by one; that is, their balance is to be directly carried forward, as opening entry, to the account of the new Ledger. By the way, we shall remark that, in his Treatise, Pacioli does not make mention of either closing or opening entries in the Journal, as we shall see below. Therefore, it seems that, in spite of what Pacioli says above, we should totally exclude the possibility that he was referring to general closing and opening entries, even if they were only to be made in the Ledger. In effect, with regard to the closing of the accounts in the old Ledger and to their opening in the new one, he expressly says in Chapter 34: “Summarai tutte lor partite in dare e havere, aiutando sempre la menore, comme te dixi sopra del portare avanti, che questo atto de un quaderno in laltro e de ponto simile a quello e fra loro non e altra differentia se non que in quello el resto si porta avanti nel medesimo quaderno, e in questo de un libro in laltro, e dove in quello chiamavi le carti d quel libro proprio in questo si chiama le carti del libro sequente,” i.e., “You will add up the debit and the credit side of all their accounts, completing always the lesser part, as I said before with respect to the carryover of accounts, since this transfer from one Ledger to another is absolutely similar to the abovementioned one and the only difference between them is that, in the first case, the balance was carried forward to a following folio of the same Ledger whereas, in the second case, it is transferred from one book to another. So, in the former, the reference mentioned was the folio of the same book and, in the latter, it is a folio of the following Ledger.”47 In view of all the
y, por consiguiente, el resumen de todas,” i.e., “Which is the last one of all the Ledgers and, thus, the summary of all.” In accordance with the approach described at the beginning of this note, Antinori translates: “Che resta sempre Vultimo di tutti, aperto nel Mastro e che e destinato a ricevere il saldo di tutti gli altri conti,” i.e., “Which is always the last one that remains open in the Ledger and that will receive the balance of all the other accounts.

47 Jager translates this passage in a rather complicated way: “Du wirst alle Posten im Geben und irn Haben summirer, inden Du die kleineren abziehst, uie ich Dir schon gesagt habe, denn dieser Akt von einem Heft in das andere ist dem anderen ahnlich, und zwischen den Beiden ist kein anderer Unterschied, als dass in diesem der Rest in demselben Heft weiter ubertragen wird, und in jenem von einem Buche in das andere; und wdhrend Du in jenem Dich aut die Blatter jenes Buches berufst Du in diesem Dich auf die Blatter des folgenden Buches berufst”, i.e.,”You will add up all the debit entries and credit entries and deduct the smaller, as I told you, since this operation from one book to the other is similar to the other one, and the only difference between them is that, in this case, the above, we must conclude that Pacioli’s words necessarily meant that the Capital account was simply the receptacle of nominal and expense accounts. At the most, in a broader sense, it could be interpreted that these words could refer to the fact that all assets and liabilities accounts were posted to the Capital at the beginning of the operations, when recording the Inventory.

In balance is carried forward in the same book and in the other one, from one book to the other; and while, in the former, you refer to the folios of that book, in the latter, you refer to the folios of the following book.” Penndorf is much clearer: “Hierauf wirst Du alle Kortten im Soil und im Haben addieren und dabei immer die kleinere Seite ergdnzen, wie ich Dir oben beim Ubertragen nach vorwarts sagte. Denn dieses Ubertragen von einem Hauptbuch in das andere ist jenem genau ahnlich und zwischen ihnen ist kein anderer Unterschied, als dass in jenem das Saldo in detnselben Hauptbuch vorgetragen wird und in diesem von einem Buche in das andere; und wahrend man sich in jenem auf die Blatter desselben Buches beruft, ruft man in diesem die Blatter des folgenden Buches,” i.e., “To do this, you will add up the debit entries and the credit entries of all the accounts, always completing the lesser side, as I told you before when explaining how to carry forward accounts to a new folio. This transfer from one Ledger to another is exactly the same as the mentioned one, the only difference being that, in the former, the balance is transferred in the same Ledger and, in the latter, from one book to another and while, in the former, you refer to the folios of the same book, in the latter, you refer to those of the following book.” With only a few changes, the translations into English of Geijsbeek, Crivelli and Brown and Johnston do not differ from Penndorfs version. The same occurs with Haulotte and Stevelinck: “Vous totalisez tous les postes du debit et tous ceux du credit d’un compte, en ajoutant toujours la difference du cote le plus petit, comme je vous Vai dit precedemment a propos du transfert des comptes, car le transfert dans un autre Grand Livre est identique. II n’existe entre les deux comme difference, que dans un cas, ib sont transferee plus loin dans le mSme livre, et dans Vautre, Us sont transferes d’un livre a I’autre. Alors que dans le premier cas on notait la nouvelle page du meme livre, dans I’autre, on note la page du livre nouveau,” i.e.,

You will sum up the debit entries and credit entries of an account, always adding the difference on the smaller side, as I told you with respect to the transfer of accounts, since transfer to another Ledger is performed in the same way. There is a single difference between both: in one case, accounts are transferred to a new folio of the same book and, in the other, they are transferred from one book to another. Therefore, in the first case, you will note the new page of the same book and, in the other, the page of the new book.” Cardenas also provides a similar translation: “Sumards todas las partidas (cuentas) en el Debe y en el Haber, ayudando (igualando) siempre a la menor, como se dijo antes en los traspasos. Este acto de pasar de un Mayor a otto, es igual al anterior, y entre ettos no hay diferencia alguna, ya que en aquel el saldo se traspasa en el mismo Mayor, y en este de un libro a otro, y mientras que en aquel indicabas las hojas de aquel libro, en este debes indicar la hoja del libro siguiente,” i.e., “You will add up all the entries (accounts) on the debit side and on the credit side, always helping (making equal) the lesser one, as mentioned before with respect to transfers. This posting operation from one Ledger to another is similar to the previous one and there is no difference between them because, in this case, however, the remark that this account is a receptacle of all the others as a consequence of the fact that it is the last one to be closed does not seem to make much sense.

The fact that no closing or opening entry is made in the Journal is confirmed, apart from the above passages, in other points of Chapters 33 and 34. In Chapter 33, Pacioli says that new business carried out while accounts are closed and transferred from the old to the new Ledger can be entered in the new books: “in lo memoriale o vero giornale, ma non in quaderno per fin tanto che non li hai portati li resti del primo quaderno,” i.e., “in the Memorandum or in the Journal, but not in the Ledger, until you have transferred the balances of the first Ledger.” In Chapter 34, he expressly specified: “E quelle (the balances) portarai in libro A, doe in quaderno nuovo, che non bisogna come fo detto di sopra li resti ponere in giornale,” i.e., “Carrying forward the balances to Ledger A, that is, to the new Ledger, then, as we said before, it will not be necessary to enter them in the Journal.

The fact that no general closing or opening entry was directly made in the Ledger, without being recorded in the Journal, is also confirmed in another passage of Chapter 34: “In modo che nel reporto de un libro in laltro, solo una volta per ciascuno quaderno se mette la partita, e questa prerogativa a lultima partita sempre deli quademi che nullaltra mai po havere,” i.e., “Thus, in the transfer from one book to another, the balance is entered only once in each Ledger. And only the last the former, the balance is transferred in the same Ledger and, in the latter, from one book to another and while, in the former, you noted the sheets of the same book, in the latter, you will note the sheet of the following book.” In spite of his idea on the general closing of all accounts as a contraentry to the Capital account, Antinori interprets this passage as the other translators: “Tu somtnerai tutte le partite a debito e a credito di un conto, aggiungendo sempre la differenza nella sezione piii piccola, come ho detto in precedenza a proposito del trasferimento dei conti, poichi il trasferimento in un altro libro Mastro e identico. Non esiste tra i due che questa differenza: nel primo caso sono trasferiti piii lontano nel medesimo libro, nel secondo, sono trasferiti da un libro all’altro. Come nel primo caso si annota la nuova pagina dello stesso libro, nel secondo, si nota la pagina del libro nuevo,” i.e., “You will sum up all the debit entries and credit entries of an account, always adding the difference on the smaller side, as mentioned before with respect to the transfer of accounts, because transfer from one Ledger to another is performed in the same way. There is only one difference between both: in the first case, they are transferred further on in the same book and, in the second, they are transferred from one book to another. Likewise, in the first case, you should note the new page of the same book and, in the second, the page of the new book.”

entry, that is, the closing balance has this prerogative in the Ledger.”48 If these words have been well interpreted, they indicate quite clearly by themselves that the account closing and transferring process did not give rise to any general entry because, if it had been so, the balances would have had a contraentry in the same Ledger. On the contrary, this process was done directly by transferring the balances, one by one, to the new accounts in the new Ledger.

In this same chapter, there is a passage that Basil S. Yamey considers as one of the most obscure points of the whole Treatise [Yamey, 1978, p. 573]. In this passage, Pacioli refers to the transfer of profit to the Capital account after closing the profit and loss account, saying that the credit balance of the latter will
48Jagcr translates these words as follows: “In dem Uebertrag von einem Buche in das andere der Posten nur ein Mai fur jedes Heft eingeschrieben wird. Diesen Vorzug
(prerogativa^Vorrecht) hat der letzte Posten der Hefte immer, und kein anderer Posten kann ihn haben,” i.e., “In the transfer from one book to another, entries are only recorded once in each book. This prerogative (prerogativa = privilege) is always given to the last entry of the books and to no other.” Penndorf translates them practically in the same way: “Beim Ubertrag von einem Buche in das andere die Buchung nur ein einziges Mai in jedem Hauptbuch erfolgt. Diesen Vorzug hat immer der letzte Posten der HaupbiXcher und kein anderer kann ihn haben.” Geijsbeek tries to specify more: “Making the transfer from one ledger to another, any account should appear only once in each Ledger. This is a peculiarity of the last entry of the accounts of the Ledgers.” The last part of the passage seems somewhat obscure to Crivelli: “In the transfer of one book to the other the accounts are entered only once in each Ledger. As you have noted here preceding, this prerogative of said Ledger accounts, no other accounts can ever have.” Brown and Johnston translate the passage in the same line as Geijsbeek. Haulotte and Stevelinck wish to be more specific: “De sorte qu’en transportant d’un livre a I’autre, on inscrit seulement un poste dans chaque Grand Livre. Ce privilege revient uniquement an poste par lequel un compte dans le Grand Livre est cloture, et d aucun autre,” i.e., “So that, when transferring from one book to the other, only one entry is recorded in each Ledger. This privilege is only given to the entry which closes an account in the Ledger and to no other.” Cardenas does a conventional translation: “De manera que los traspasos de un libro a otro, se pone la partida una sola vez en cada cuenta del Mayor; esta prerrogativa la tiene la ultima partida del Mayor y ninguna otra mds podrd tenerla” i.e., “So that in transfers from one book to another, the entry is recorded only once in each Ledger account; this prerogative is given to the last Ledger entry and to no other.” Antinori introduces a rather strange variation: “In modo che trasferendo da un libro all’altro, si iscrive solo una posta in ciascun Mastro. Questa prerogativa e caratteristica unicamente dell’ultima partita del conti o del libro Mastro, perche in nessun altro libro pud accadere,” i.e., “So that when transferring from one book to the other, only one entry is recorded in each Ledger. This prerogative is an exclusive feature of the last entry of the accounts or of the Ledger because it cannot appear in any other book.”

be entered on the debit side and transferred to the Capital account “in havere insiemi con laltre robbe, tnobili e stabili,” i.e., “on the credit side, together with the other merchandises, personal and real goods.”49 Once again, these words may lead one to think that the amounts of the assets accounts have been credited to the Capital account as a closing entry. However, we have already seen that it was not so. Therefore, we should interpret, this time with even greater certainty than in the previous case, that Pacioli merely referred to the fact that the Inventory entries were posted, one by one, to the credit side of the Capital account when the Inventory was recorded at the beginning of the operations. This is precisely the circumstance mentioned earlier.

49 Jager also attributes this meaning to the passage: “In diesem (dem KapitalConto) wiirdest Du den Posten in’s Haben eintragen, wo alle andere Sachen, Mobilien und Immobilien sind,” i.e., “You will note the entry on the credit side in the Capital account where are entered all the other things, personal and real property.” PenndorFs translation is quite similar with a few minor changes: “Wo Du (in the Capital account) ihn im Haben tusammen mit anderen Waren, Mobilien und Immobilien eintragen wirst,” i.e., “Where you will record it on the credit side together with other merchandises, personal and real property.” Geijsbeek also translates the passage in the same way: “Making the entry in the credit side (of the Capital account) where all the other goods of yours have been entered, personal or real.” Crivelli says practically the same: “You may then enter the balance to the Capital Account where the other goods, furniture, and buildings have been entered.” Brown and Johnston introduce a small change: “Credit the same amount to Capital on the same side in which all other personal and real possessions have been entered.” There are hardly any differences in the translation provided by Haulotte and Stevelinck: “Le compte Capital auquel il est porte (the balance of the profit and loss account) au credit, ou tous vos autres biens ont 6te inscrits,” i.e., “The Capital account on whose credit side, where are recorded all your other goods, it is transferred.” Cardenas translation is identical: “Abonando a la cuenta del Capital en el Haber, junto con las otras cosas muebles, inmuebles, etc.,” i.e., “Entering it in the Capital account on the credit side, together with the other things, personal, real, etc.”. Antinori does not make any new contribution: “// conto Capitale al quale e portata (the balance entry) a credito, ove tutti i tuoi altri beni sono stati scritti,” i.e., “The Capital account in which it is entered on the credit side where all your other goods have been recorded.”
50 When explaining how, after transferring the balances of nominal and expense accounts, the profit and loss account will show the profit or loss originated by our business, Pacioli says: “E veduto que harai per questa lutile e danno tuo sequito, alora questa saldarai in la partita del Cavedale, dove nel principio del tuo manegio ponesti lo inventario de tutta la tua faculta,” i.e., “And once you have seen the profit or loss incurred, you will balance it in the Capital account to which you posted the inventory of all your wealth at the beginning of your operations.”

HerndndezEsteve: Obscure Points ofDe Computis Et Scripturis 61
In this same paragraph, Pacioli insists again that the Capital account must be the last account in the entire Ledger (“in questo cavedal quale conviene essere sempre lultima partita d tutti li quaderni”). This statement should be understood in the sense that it must be the last account to be closed.51 The continuation of this sentence, which clarifies its full meaning, has also created some headaches. In fact, it says: “in questo cavedal . .. porrai sempre cognoscere tutta tua faculta giongnendo li debiti e crediti che in libro A portasti,” i.e., “from this capital . .. you can always know what your net worth is, since it contains the debit and credit balances that you have carried to ledger A.” However, the meaning of the gerund giongnendo, with its causative connotation, has not always been correctly understood.

Another passage in Chapter 34 that has also raised difficulties and created some confusion refers to the transfer of the Capital account to the new Ledger. Pacioli says in this respect:

51 Jager skips this sentence in his translation. Penndorf translates it literally:

In diesem Kapitalkonto, das immer das letzte von alien Konten der Hauptbucher sein muss,” i.e., “In this Capital account which must always be the last of all Ledger accounts.” Geijsbeek does the same: “Which must always be the last account in the entire Ledger.” Crivelli and Brown and Johnston provide a simi lar translation. Haulotte and Stevelinck interpret that it must be the last account to remain open in the Ledger: “Le compte de Capital, qui doit toujours rester le dernier compte ouvert dans le Grand Livre,” the same as Antinori: “Che devesempre restore I’ultimo conto aperto nel Mastro,” i.e., “Which must always be the last account to remain open in the Ledger.” Cardenas follows the letter of the
text: “Que siempre conviene que sea la ultima cuenta de todos los libros Mayores,” i.e., “Which should always be the last account of all the Ledgers.

52 For instance, Jager translates this passage as follows: “Du wirst folglich im Kapital stets von Deinem ganzen Vermogen Kenntnis nehmen konnen, wenn Dudie Schulden mit dem Guthaben (crediti pi.) vergleichst, wie Du diess in das Buch A etc. ubertragen hast,” i.e., “Therefore, from the capital you will always know your fortune, if you compare the debits with the credits that you have transferred to ledger A.” Penndorf translates the sentence in a completely different and original way: “In diesem Kapitalkonto…wirst Du immer von neuem Dein games Vermogen erkennen konnen, wenn Du die Schulden und Aussenstande, die Du in das Buch A eingetragen hast, hinzuzufugst,” i.e., “From this capital account
you can always know your fortune, if you add the debts and the accounts receiv able that you have carried to ledger A.” Geijsbeek translates: “Therefore, from the capital account, .

. . you may always learn what your fortune is, by adding together all the debits and all the credits, which you have transferred in Ledger A.” The translation of Crivelli is similar: “Said Capital Account … will always enable you to know the value of the whole of your property, providing you add the debits and credits which you have transferred to Ledger A.” The interpretation of Brown and Johnston is freer and more correct, although it goes far beyond Pacioli’s words: “From the Capital account, therefore, . .. you may learn

“E portarala (the Capital account) come laltre net quaderno A in resto e summa, o voi a partita per partita che lo pot anche fare, ma si costuma farla in summa perche una volta tutto tuo inventario apare! There is no unanimity on this point,53 but I have interpreted this passage as follows: “And you will carry it forward, the same as the other accounts, to Ledger A, and you

the entire value of your property. The value of your business appears in the Capital account as the net of all debits and credits transferred to Ledger A as well as the other accounts closed into Profit and Loss and then into Capital.” Haulotte and Stevelinck keep closer to Pacioli’s words and transmit correctly their meaning: “Ainsi, par le compte Capital . . . vous pouvez toujours connaitre Vetat de votre fortune, puisqu’il vous donne les totaux des debits et des credits que vous avez transportes au Gran Livre A,” i.e., “In this way, from the capital account … you can always know the amount of your property, because it shows the total of the debits and credits that you have carried to ledger A.” Carlo Antinori offers a completely similar translation: “Cost dal conto Capitate … tu puoi sempre conoscere lo stalo del tuo patrimonio, poiche ti da i totali delle attivitd e delle passivita che hai trasportato nel Mastro A,” i.e., “So, from the capital account . . . you can always know the amount of your property, because it shows the total of the assets and liabilities that you have carried to ledger A.” On the contrary, Cardenas turns back to an interpretation similar to that offered by the first translators into English: “Y de nuevo, en la de Capital . . . podrds siempre conocer todo tu patrimonio (facolta), anadiendo las deudas y los creditos que pasaste en el libra A,” i.e., “And once again, from the capital . . . you will always be able to know all your property, by adding together all the debts and credits that you have carried to ledger A.

53 Jager translates this passage as follows: “Und denselben wie die andern in das Heft A in Rest und Sumtne, oder Posten per Posten ubertragen. Man pflegt aber den Posten in Sumtne zu ubertragen (fare) weil alsdann Dein ganzes Inventor” i.e., “You will transfer it, as the other ones, to Ledger A, in balance and total or entry by entry. It is, however, customary to carry forward the total amount of the entry so that all your inventory may appear at once.” In this respect, Jager points out in a footnote that in this context “inventory” should be interpreted as “Schlussinventar,” i.e., “closing inventory” or “final inventory,” although he explains that Pacioli did not make that explicit but that he identified it with the results of the Capital account. Penndorf interprets this passage in a similar way: “Es wie die anderen in das Hauptbuch A in Saldo und Sumtne oder, wenn Du willst, Posten fur Posten ubertragen, was Du auch tun kannst. Aber man plegt es in einer Summer zu tun, weil sodann Dein ganzes Inventor mit einem Male erscheint,” i.e., “As the other ones, you shall transfer it to Ledger A in balance and total or, if you wish, entry by entry, since you can also do it this way. However, it is customary to transfer the total amount, since this allows to see your entire inventory at once.” Geijsbeek remains in the same line: “Then this capital account should be closed and carried forward with the other accounts to Ledger A, either in total or entry by entry. You can do either way, but it is customary to transfer only the total amount, so that the entire value of your inventory (inventario) is shown at a glance.” Neither Crivelli, nor Brown and Johnston introduce any change in their translations, whereas Haulotte and Stevelinck introduce an ingenious one in theirs: “Ensuite ce compte Capital du

may transfer the balance or the total amount of debit and credit sides, or even, if you wish, entry by entry. But it is customary to transfer the total amounts of the account since they show the whole Inventory at a time.” With respect to the possibility, which seems quite odd to us, of transferring the Capital account entry by entry, it should be pointed out that Pacioli does not mention whether the Inventory should be made each time the Ledger is closed. It seems rather the opposite. In Pacioli’s opinion, the closing of the Ledger should be made every year, without awaiting the completion of the book.

In Chapter 36, another expression has raised some doubts, which says: “El bilancio del libro debbe essere pan, cioe che tanto debbe esser la summa non dico de creditori ne debitori, ma dico la summa del credito quanto la summa del debito,” i.e., “The Ledger balance must be reconciled, that is, the total amount, I do not mean of creditors and debitors but of credit, must be equal to the total amount of debit.” It seems that Pacioli wants to make it clear that what are to be reconciled in this bilancio are not the Ledger credit and debit balances but the total amounts of debit and credit entries. Practically all translators agree on this point.54 On the other hand, he already mentioned in Chapter 34 that all the total amounts of debit entries and all the total amounts of credit entries of the accounts in the Ledger had to be recorded separately in a folio. Then, the total amounts of debit entries, on one hand, and those of credit entries, on the other, were to be added up, the totals being called summa summarum of debit entries and summa summarum of credit entries, respectively. These two summe summarum had to be

Grand Livre Croix sera cloture et transports au Grand Livre A, soit pour son solde, ou si vous le preferez, porte poste par poste; quoiqu’on ait Vhabitude de le faire en une somme, parce qu’alors votre fortune est inscrite en une fois,” i.e., “Then, the Capital account of the Ledger of the Cross will be closed and carried forward to Ledger A, either in balance or, if you prefer, entry by entry, although it is customary to transfer the total amount since in this way your wealth is recorded all at one time.” Cardenas does not make any new contribution. Carlo Antinori translates this passage as follows: “In seguito, questo Conto Capitate del Mastro Croce sara chiuso e trasportato net Mastro A, sia per it suo soldo, o se lo preferisci, portando partita per partita. Qualcuno ha Vabitudine di fare una somma, ed in questo caso il tuo patrimonio e rappresentato in una sola volta, dal suo ammontare.”
54 However, Carlo Antinori’s interpretation of this passage has nothing to do with total amounts and balances but with the number of debit and credit accounts: “II bilancio del Libro deve essere pan, cioe pan devono essere le somme, non del numero dei creditori e dei debitori, ma le somme del crediti e dei debiti.”

equal if the Ledger was well kept and balanced.55 Pacioli points out that he had anticipated this conclusion in Chapter 14, where he also explained its reasons. In fact, in this chapter it is explained that each Journal’s entry originates two entries in the Ledger, one on the debit side and another on the credit side. In the same way, he indicates: “di qua nasci poi al bilancio che del libro si fa nel suo saldo tanto convien che sia el dare quanta lavere,” i.e., “this is the reason why, afterwards, in the balance that is stroken at the moment of the closing the book, the debit must come to the same amount as the credit.” We shall return at once to the mentioned passage of Chapter 34 in relation to another serious and interesting problem. For the moment, let us just say that, in both cases, the total amounts in question do not seem to always reflect the total movement of the accounts because Pacioli does not say anywhere that total amounts should also be transferred when carrying forward the balance of an account to a new folio because the current one is full. It seems rather that the opposite practice was in use at that time. Therefore, the total amounts of debit and credit entries appearing in the swnma swnmarum of Chapter 34 and the bilancio of Chapter 36 should, in any case, be the total amounts of the last folio of the account.

“E acio sia piu chiaro de ditto saldo, farai questo altro scontro. Cioesummarai in un foglio tutto el dare del quaderno croci, e ponlo a man sinistra. Esummarai tutto suo havere, e ponlo a man dextra. E poi queste ultime summe ressummarai e farane de tutte quelle del dar una summa che si chiamara summa summarum. E cosi farai una summa de tutte quelle dal avere che si chiamara ancora lei una summa summarum, ma la prima sira summa summarum del dare e la seconda si chiama summa summarum de lo havere. Or se queste doi summe summarum siran pare, cioe che tanto sia luna quanta laltra, videlizet quella del dare e quella delo havere, arguirai el tuo quaderno essere ben guidato, tenuto esaldato.

However, in the example of summa summarum inserted by Manzoni in his book Quaderno doppio col suo giomale, at the end of the Ledger assumption, and although under the name of Summa delle Summe, the names of all the Ledger accounts are written in an ad hoc page after closing the accounts. Both outstanding and carried forward accounts appear by strict order of folio followed in the relevant line, first, by the sum of the debit entries of each account, and then, on the right hand side, by the sum of the credit entries, which is
obviously equal. At the end of the page appears the Summa delle Summe with the reconciled totals of the debit and credit sums. This list occupies almost four complete pages of Manzoni’s work at the end of which he totals the Summa delle Summe of each of them, obtaining in effect the total of all entries, i.e., of all the Ledger movements, since this total also includes the sums of the accounts carried forward to a new folio.

DOUBTS ON THE TREATISE AS A SINGLE UNIT

Regardless of any possible accusation of plagiarism, the truth is that a thorough reading of Luca Pacioli’s Surnma de Arithmetica, Geometria, Proportioni et Proportionalita gives the clear impression that it is not a single work written from start to finish but a collage of heterogeneous elements written in different occasions and for different purposes which have been juxtaposed.

In the same way, a careful study of the Particular Treatise De Computis et Scripturis, included as “Title Nine, Treatise Eleven” of Pacioli’s Summa, gives grounds for believing that neither is this Treatise a single work written at the same time and for the same purpose. On the contrary, the Treatise seems to be made up of at least two separate parts showing a number of clear differences: on one hand, the first thirtyfive chapters constitute a single unit and, on the other, Chapter 36 which is introduced as a summary, as well as the two following sections that have a heading but no number, together with an example, provided at the end, consisting of ten related Ledger entries. Some authors believe that all of it could be considered as part of Chapter 36.57 An additional reason, not argued so far, to link Chapter 36 proper to the final parts of the Treatise could be that, both in the examples with money amounts provided in that chapter and in all the Ledger entries presented at the end, the monetary unit is not the one expressly adopted throughout the first thirtyfive chapters, i.e., the gold lira de grossi divided into soldi, grossi and piccioli but the lira divided into soldi and denari which was the monetary unit used by Florence accountants. It should also be pointed out that the entries recorded in the Cash account in this final example do not include any explanation as it was recommended in Chapter 36. Likewise, in the first unnumbered section headed Casi che apartieni a mettere al libro de mercanti of this final part, a direct and express reference is made to a passage of Chapter 36.58 Some believe, however, that Chapter 36 is independent of the two unnumbered sections that

“This is what Carlo Antinori does in his version of Luca Pacioli’s Treatise into modern Italian.

58 This reference reads as follows: “e come nelle regoie to ditto tutte U partite vogliono havere in loro tre cose, cioe it giorno e la quantita de la pecunia e la cagione.” The expression regoie refers to the title of Chapter 36, “Summario de regoie e modi sopra il tenere uno libro di mercanti” in whose first p>aragraph these three requirements are indeed specified.

follow it, which in their opinion seem to be afterthoughts that Pacioli adds to the text to complement it.59 Anyway, the question is still whether these afterthoughts refenred to the first thirtyfive chapters or to Chapter 36. One thing seems to be clear: these four sections or elements do not seem to be integrated in the main body of the Treatise but juxtaposed afterwards, even if Pacioli mentions their existence in previous parts of his text, as we shall see. For this reason, they can be considered a sort of appendix to the Treatise, whether or not they form a separate unit per se, since they present some clear differences with regard to the first thirtyfive chapters which make up the main body of the Treatise.
Many years ago, it was observed that the group of ten entries was formulated, as already pointed out, following the Tuscan model and, therefore, differed from the examples provided in the text of the first thirtyfive chapters, which were written according to the Venetian practice [Besta, 1916, p. 361]. Yet until now, not much attention has been paid to the fact that the differences arise not only in this group of entries but in the entire appendix. Only Basil S. Yamey noticed and pointed out some of these differences, even observing in passing in a halfjoking tone — that those who consider Pacioli a plagiarist could find reason to say that when the Franciscan friar wrote his Treatise, he not only plagiarized one work but two [Yamey, 1978, p. 577].

The division of the Treatise into two or more differentiated parts does not necessarily lead to the conclusion that they were written by different authors. Rather, it could simply be concluded that the parts of the appendix had a different origin than the main body of the text and that they were written at a different time and for a different purpose. Specifically with regard to Chapter 36 (to which the author refers in Chapter 12 and 34 explaining that it contains a summary of the preceding chapters), it is possible that Pacioli wrote it on another occasion, before or after writing the body of the text, in order to give to specific, possibly Tuscan, readers an abridged explanation of the rules that had to be followed by a merchant to apply doubleentry bookkeeping to his accounts. Later, when he wanted to publish the Summa and gave it to his printer, he would decide to use the text to complete his Treatise. At any rate, he mentions the existence of this summary in Chapters 12 and 34, as well as in the sumario dela terga parte principale which appears? at the beginning of the Summa de Arithmetica, Geometria, Proportioni et Proportionalita (unnumbered folios 4 v” and 5 r2). In the opinion of Basil S. Yamey, the ten related Ledger entries were also referred to by Pacioli, though somewhat cryptically in Chapter 15 saying: “e anco in fin di questo harai exemplo,” i.e., “and at the end of this you will also find an example.

Let us now see what are the main differences observed. In the first lines of Chapter 36, it is said that “lultimo nome dela partita del debito debbe essere il primo della partita del credito,” i.e., that “the last name of the debit entry must be the first of the credit entry.” This condition is met, in effect, in the Ledger entries provided at the end. These entries, formulated according to the Tuscan style, are written, for instance, as follows: “Ludovico di Piero Forestani owes on 14 November 1493, L. 44. S. 1. D. 8, for an amount in cash borrowed by him, and I enter it on the credit side of the Cash account, in folio 2.” However, in the examples provided in the text of the first thirtyfive chapters written in the Venetian fashion, this rule is not so obvious, as we can see when considering one of these entries: “Cash account owes on 8 November to Capital account, for various types of cash, in gold and coins, custodied in same, today, in total, folio 2.” As can be seen in the Ledger entry, according to the Tuscan model, the heading of the contraentry account is placed at the end of the explanation, just before specifying the number of the relevant folio. On the contrary, in the Venetian style, the Ledger entry in the debit account is practically the same as the Journal entry. The contraentry account is placed immediately after the holder’s account or, at most, after the date.

A little further, it is explained that: “Lo bilancio del libro sintende un folio piegato per lo longo,” i.e., “By Ledger balance we understand a folio folded lengthwise.” In the previous chapters, it is not mentioned that this folio should be folded. On the other hand, neither in Chapter 36, nor in the following sections, is it mentioned that this balance is called summa summarum, as opposed to Chapter 34 where this name is strongly emphasized. It was shown above that the total amounts of debit entries and
60 This opinion has also been expressed by Yamey in his comments to this paper.

credit entries were recorded both in the summa summarum of Chapter 34 and in this bilancio of Chapter 36, with the remark that these total amounts do not seem to reflect the total movement of the accounts but only that of the last folio. On the other hand, it seems that balances had to appear also in the bilancio, in addition to total amounts.
When explaining in Chapter 36 how to write the balance in a folded folio, Pacioli specifies: “sul quale dala mano destra si copiano li creditori del libra, e dala sinistra li debitori. E veda se la summa del dare e quanto quella de lavere. E allora il libro sta bene,” i.e., “in which you will put down the credit balances of the Ledger on the right hand side and the debit balances on the left hand side. And check if the total amount of debit is equal to that of credit. If it is so, the Ledger is correct.” As mentioned before on another passage in this same chapter, Pacioli strongly insisted that the expressions creditori and debitori referred to balances, whereas the total amounts of debit entries and credit entries were called summa del debito and summa del credito. These were precisely the total amounts of the bilancio that had to be reconciled and not simply those of the balances. Therefore, it seems that it can be concluded that both the total amounts and the balances of the accounts had to appear in the bilancio of the Ledger analyzed in Chapter 36. This conclusion is obviously based on the assumption that Pacioli used these terms accurately and in a systematic way, but we cannot always be sure of that.

In support of the theory that account balances had to appear also in the bilancio explained in Chapter 36, we shall recall that in Chapter 34 it was said that accounts were to be transferred directly from the old Ledger to the new one, from book to book, without any other contraentry or Journal entry. This procedure is not basically contradicted in Chapter 36 but an intermediate step is introduced when it is explained that the accounts of the old Ledger must be closed and those of the new one opened taking off the balances recorded in the bilancio. The passage says: “E di poi levare el bilancio del libro vechio, che sia giusto e pan come debba essere, e da quello bilancio copiare tutti li creditori e debitori in sul libro nuovo, tutti per ordine, come elli stanno in sul bilancio,” i.e., “You will then strike the balance of the old Ledger and duly reconcile it. Afterwards, you will take off all the creditors and debtors from this balance and will post them to the new Ledger, in the same order in which they appear in the balance sheet.” Pacioli says further on: “E in ciascuna partita del debitore hai a dire per tanti resta a dare al libro vechio segnato A,” i.e., “In every entry transferring a debtor’s account you must say: for so much that remains to owe according to the old Ledger marked with an A.”61 Similar instructions are given to close the accounts of the old Ledger, always after opening the new ones in the new Ledger.

On the other hand, this indicates that, while the summa summarum was the ultimate check to make sure that the accounts of the old book had been closed and those of the new one opened correctly and that it was, therefore, established after this process was completed (as pointed out by Edward Peragallo) [1938, p. 59], the bilancio described in Chapter 36 was drawn before transferring the balances to the new Ledger. The summa summarum and bilancio were not the same document, had different names and were presented, if the hypothesis suggested in this paper is true, in two different texts that were juxtaposed later on.62 All of this gives reason to believe that the summa summarum mentioned by Pacioli in Chapter 34 and the

However, in his mentioned work: “La cldture des comptes dans la Summade Arithmetica,” Pierre Jouanique considers that the bilancio of Chapter 36 did not show the balances but only the total amounts. Balances would be transferred to open the new Ledger and to close the old one on the basis of the total amounts recorded in same but directly from the accounts of the old Ledger, in a sui generis interpretation of Pacioli’s words.

It seems that this fact had not been observed so far by scholars although, in a very recent article, Pierre Jouanique expresses his conviction that these two balances were completely different, saving that: “// ne faut pas confondre lebilancio du chapitre 36 avec la summa summarum du chapitre 34. Cette derniere se place a la fin des operations de cldture, et a pour objet de verifier qu’elles ont eti correctement effectuees,” i.e., “The bilancio of Chapter 36 should not be mixed up with the summa summarum of Chapter 34. The latter is drawn
at the end of the closing operations and its purpose is to check that they have been carried out correctly.” (See his work: “La cldture des comptes dans la Summa de Arithmetica,” quoted work). However, Jouanique develops his reasoning as if Chapters 34 and 36 were part of a consistent and coordinated whole, since he does not realize that, as explained, they possibly belong to two different bodies written separately. This is precisely the explanation of many of the inconsistencies and difficulties met by scholars. Jouanique believes the two balances were part of the same process: first, the bilancio of Chapter 36 was drawn, then accounts were closed and opened and, at the end of the process, the summa
summarum was established as a final check.

According to Jouanique’s approach, closing operations, as described by Pacioli, could be divided into six steps:

1. To crosscheck Journal and Ledger entries;
2. To close Ledger accounts and point out balance entries by means of the abbreviation R° in the margin;
3. To establish a balance to check total amounts (the bilancio);
4. To carry forward bilancio described in Chapter 36 were conceived in a different way and had a different purpose.

At this point, it is important to remember that, as observed by others (e.g. Basil S. Yamey [1978] and Edward Peragallo [1941, p. 448]), Pacioli used the word bilancio to mean not only the statement of total amounts or balances recorded in the mentioned folio, folded or not, but also used it in the broad sense to designate all the Ledger closing operations as a whole, whether the book was closed because it was already full or at the end of the financial year, as it was customary in some places. Pacioli says in Chapter 32: “Bisogna hora dar modo al reporto de un libro in laltro quando volesse mutar libro, per cagione che fosse pieno o vero per ordine annuale de milesimo, come el piu si costuma fare per luochi famosi che ogni anno, maxime a milesimi nuovi, li gran mercatanti sempre lo observano. E questo atto insiemi con li sequenti e detto el bilancio del libro,” i.e., “It is necessary to talk now about the way to post entries from an old Ledger to a new one when you have to change book, either because the previous one is full, or because of the annual closing of accounts, as it is customary in important places where big merchants always change books once a year at the beginning of the new year. And this operation, together with those that will be explained below, is called to make the balance of the Ledger.” On the other hand, this passage led Mathieu de la Port and Pierre Jouanique more than two hundred years later, to observe that Pacioli distinguished two different reasons to close the books. As pointed out by Mathieu de la Porte, this gave rise to different processes [Jouanique].

In this sense, going beyond the mentioned differences between the summa summarum of Chapter 34 and the bilancio of Chapter 36, it seems as if, as a whole, the closing process discussed in the first part of the Treatise was different from that described in the summary. While it seems that a true closing of the financial year is considered in the body of the Treatise, with the results being settled and incorporated into the Capital account, by contrast, the summary seems to describe a simple transfer of accounts from an old Ledger to a new one after having checked, of course, if the entries are correct. In any case, it must be pointed out that the accounts of merchandise entries
balances to the new Ledger; 5. To regularize expense, commission and, if required, Cash accounts and to adjust profit and loss and Capital accounts; 6. To strike a final trial balance, the summa summarum.

totally sold are settled and their results transferred to the profit and loss account, when the last lot is sold, without awaiting the closing of the financial year. At any rate, the steps to be identified in the closing process discussed in the body of the Treatise would be the following, described in order:

1. Crosschecking and ticking all entries of the Memorandum and any subsidiary books, of the Journal and Memorandum entries and, finally, of the Ledger and Journal entries;

2. Closing of Ledger accounts, except the Capital, expense and nominal accounts, calculating the balances and adding the debit entries and the credit entries of each folio,
already equalled, so that it can appear at first sight thatthey are reconciled;

3. Transfer of the balances of these accounts directly to their respective folio in the new Ledger;

4. Closing of expense and nominal accounts following the same procedure;

5. Transfer of the balances of these accounts to the profit and loss account;

6. Closing of the profit and loss account following the same procedure and transfer of its balance to the Capital account;

7. Closing of the Capital account in the same way and transfer of this account, carrying forward its balance or total amounts or each single entry to the respective folio in the new Ledger;

8. Striking of the sumrna summarum, as final balance of total amounts for checking purposes, posting the final total amounts of each account, that is to say, the amount
of debit entries and the amount of credit entries after having equalled them in order to close the account, as interpreted by Edward Peragallo, or the amounts before recording the balance on the opposite side.

These would be the steps required to close the accounts and to strike the balance, as explained in the first part of the Treatise, i.e., in the first thirtyfive chapters.
In the closing process considered in the “Summary,” many of these steps are omitted, besides referring to a different balance. Thus, nothing is said about the closing of nominal and expense accounts by transferring their balance to the profit and loss account or about the closing of the latter by transferring its balance to the Capital account. According to the summary, the closing of the Ledger “quando el libro fusse pieno o vechio e tu volessi ridullo a un altro libro,” i.e., ” when the book is full or old, and you wish to transfer it to a new book,” would consist of the following steps, in this order:

1. Striking of the balance of the old book, recording the debit amounts on the left and the credit amounts on the right;

2. Reconciliation of the balance, that is, “eke sia giusto epan come debba essere,” i.e., the total amounts of debit entries must be equal to those of the credit entries, as
expressly stated by Pacioli: “La summa, non dico de creditori ne debitori; ma dico la summa del credito quantola summa del debito;”

3. Transfer of balances of credit and debit accounts from the balance sheet to the new book, in order, as they appear in the balance sheet or bilancio, posting the respective balance as opening entry of each new account;

4. Closing of the accounts of the old Ledger by posting the respective balances taken off from the balance sheet to the relevant accounts, as closing entry, on the opposite
side in order to equal both sides and to cancel the account.

This is all the “Summary” says with respect to the closing of accounts or, rather, to the transfer of accounts from an old to a new Ledger.

Without realizing that Pacioli possibly refers not only to one balance but to two different balances, scholars have expressed different opinions with respect to the nature of the balance presented in the Particular Treatise De Computis et Scripturis. Given the circumstances, it is not surprising that there have been opinions to suit every taste. To most of these scholars, the balance referred to by Pacioli is a mere trial balance. To others, it is more than that, because they believe it shows some typical traits of a yearend balance. Finally, in the opinion of a few, it is not even a true trial balance. All depends, obviously, on which features their opinion is based: those of the bilancio explained in Chapter 36 or those of the summa summarum of Chapter 34. It should be stressed once again that all the analyses are largely based on the reliability to be attributed to the expressions used by Pacioli in terms of accuracy, uniformity of the incorporated concept, etc. If these conditions are not met, the analyses become a simple play on words. At any rate, if the analysis is based on the summa summarum that Pacioli himself considers as the ultimate check, it seems in principle clear that, as it is a balance of total amounts, without account balances, it should be considered just a trial balance. However, as already mentioned, the summa summarum was established after having made all the adjustments required to settle the results obtained in the financial year, both from purchases and sales of merchandise, carried out as the lots were completely sold, and from expenses incurred. If one did not perform all the adjustments that would be carried out today in relation to the evaluation of stocks, the amortization of personal and real property, the requalification of debtors, etc., this is by no means attributable to the balance procedure but to the general accounting approach. For this reason, Carlo Antinori says that the balance mentioned by Pacioli is something more than a trial balance [Antinori, 1990, p. 7]. It should be mentioned in passing that among the specific adjustments omitted by Pacioli in his Treatise, are those related to cash funds retired at one stroke to pay small expenses little by little, as well as to the lots of merchandise not yet totally sold.

To Edward Peragallo, on the contrary, the balance explained by Pacioli is not quite a true trial balance. Peragallo refers only to the summa summarum and does not seem to see the differences between the latter and the bilancio of Chapter 36, which he does not mention. He says that the summa summarum cannot be a trial balance, since it is established after closing the accounts of the old Ledger and opening those of the new one and, therefore, after having balanced the accounts and entered their balance on the opposite side. He argues that, in these conditions, if the total amounts of each account are reconciled and equalled, the general total amounts must also be reconciled and equalled, this last step representing no check at all. For this reason, in his opinion, the summa summarum is established for the exclusive purpose of checking the correctness of the closing of the ledger, i.e., that no account has remained unbalanced.63 Peragallo is right. We should admit the possibil

63 “Obviously, a trial balance of a closed ledger is no trial balance ait all. It is bound to balance in all cases, even if the ledger were full of errors, because both sides of the accounts were made equal by transferring their balance to the new ledger. It is clear that Paciolo did not know the true function of the trial balance nor its proper construction. This leaves only one possible alternative, that ity, however, that although the summa summarum is certainly established as the final step of the whole closing’, process of the Ledger and the financial year, the total amounts considered in same could be not the final ones of the accounts, already made equal, but those established before recording the balancing entry. Nevertheless, this possibility seems to be highly improbable, taking into account the example of Summa delle Summe inserted by Manzoni in his book discussed earlier.

If the bilancio mentioned in Chapter 36 is taken as a basis, we must admit that, although both total amounts and balances apparently appeared in it, taking into account that it is not said that nominal and expense accounts were previously adjusted and that the profit and loss account was balanced with a contraentry in the capital account, the bilancio can hardly be considered as anything more than a trial balance. According to what Pacioli says in this context, this bilancio was strictly used, first, to check that the old ledger had been kept correctly and, then, to post the opening entries to the new Ledger as well as the closing entries to the old Ledger.

It should also be pointed out that Chapter 36 does not mention at all that the date should appear either in these balancing, closing entries, or in the opening ones. In the examples provided, the date is not indicated in any of these entries. In Chapter 34, however, it is specified that these entries should mention the date on which the balance is drawn.
We turn now to another question. In Chapter 36, it is also stated that the entries carried to the Cash account can be written in an abbreviated form, “doe senca dire la cagione, solamente dire da tale di tale, o a tale di tale,” i.e., “without specifying the reason, saying only from Soandso on such day, or to Soandso on such day.” This is new with respect to previous chapters.

It is also mentioned that any new account should be opened “in carta nova, senca tornare a dietro, ancora che a drietro vi trovassi spacio da metterla. Non si die scrivere in drietro, ma sempre avanti, per ordine, come vanno li giorni del tempo che mai non ritornano in drietro,” i.e., “in a new folio, without going back, even if there is space for it. When opening account, you shall not go back but always move forward, in order, the same

Paciolo was using his ‘summa suxnmarium’ for exactly the purpose he describes — to prove the correctness of the closing of the ledger, and not for the purpose of a trial balance in the modern sense.” [Edward Peragallo: “Origin of the Trial Balance,” quoted work, p. 449].

as days never move back.” Although the same idea is expressed in previous chapters, and especially in Chapter 28, it is perhaps not stated in such an explicit and categorical way. These words obviously do not mean that two or three accounts cannot be maintained in the same folio if their movement does not require more space, as it is confirmed later in this same Chapter 36 when Pacioli says: “E lascia a ciascuno tanto spatio quanta tu arbitri havere a travagliare con seco,” i.e., “And leave for each of them as much space as you think you will need for the operations you intend to carry out with them.

In relation to the contraentries made to cancel and correct errors, it is specified that they shall be distinguished with a cross or an H. In Chapter 31, when discussing this subject, Pacioli only recommended to put a cross, although he added “o altro segno,” i.e., “or another sign.” Therefore, the H is mentioned here for the first time.

With respect to balancing entries made to carry forward an account to a new folio, it is expressly indicated that these entries are written “senca mettere giorno,” i.e., “without recording the day” and this is how they appear in the example provided. The same is said for the entry through which the balance is carried forward and the account is opened in the new folio, although in this occasion the example says: “Tale di tale d tali de havere.” Considering the above, this sentence should be translated as follows: “Soandso has to have” and not as “On such day Soandso has to have.” In contrast, in the examples given by Pacioli in relation to the same subject in Chapter 28, the day is mentioned in both cases.
On the other had, these types of entries “si debe segnare in margine davanti cosi cioe R°, che significa resto,” i.e., “must be distinguished in the preceding margin in this way: R° which means resto (balance).” No mention whatsoever to this sign appears in the previous chapters.

When using the letters of the alphabet to designate the successive books in order to distinguish them one from the other, the summary does not mention the denomination Ledger of the Cross which, according to the former chapters, was currently used among Catholics to designate the first book. In Chapter 36, the first book is directly called Ledger A.
I should also mention in passing that the fact that the closing entries in the old Ledger and the opening entries in the new one, as well as other entries, were not entered in the Journal shows very clearly the operational and probative character of this book in which the main items to be recorded were transactions related to third parties. Examples of other entries include the closing of merchandise accounts, kept according to the periodic inventory system with a single account, the closing of nominal accounts by transferring them directly to the profit and loss account in the Ledger and the closing of this profit and loss account by transferring its balance to the Capital account. All of these are made without any entry in the Journal.

As mentioned before, the two examples with money amounts provided in Chapter 36 referring, on the other hand, to the correction of an error and, on the other, to a balance carried forward, to do not use the monetary unit expressly adopted “al modo nostro venitiano” throughout the first thirtyfive chapters, i.e., the gold lira divided into soldi, grossi and piccioli, but the lira divided into soldi and denari used by Florentine merchants in their accounts. We have already seen that the same occurs in the ten interrelated Ledger entries provided as an illustrative example at the end of the Treatise.

A basic difference between this part of the Treatise and the previous one appears in relation to the Capital account. In the body of the Treatise, the first thirtyfive chapters, the Capital account is always and consistently used under this name — “Cavedale.” In the first unnumbered section after Chapter 36, which is entitled “Casi que apartiene amettere al libro de mercanti,” i.e., “Cases that must be recorded in the merchants’ book,” instead of the Capital account, the expression used every time is “Tuo conto, doe tu medesimo,” i.e., “Your account, that is yourself,” etc. The denomination Capital account is never used, neither in this section, nor in any other one in the appendix, which starts in Chapter 36.64
Another novelty which appears in the appendix with respect to the previous part of the Treatise is the recommendation made in this first unnumbered section that no entry is to be made for inventory goods whose value is less than ten ducats, since such goods are not to be included in the Ledger: “Ma nota che queste partite sintende che non sienno manco di died ducati luna, pero che le cose minute di poco valore non si mettano al libro.

This section also mentions for the first time ship insurance operations whose premiums received in cash are credited to an account bearing a proper name, “sicurta di navilij,” and debited to the Cash account. The same occurs with merchandise received on consignment to be sold against a commission, an operation that had never been mentioned in the first thirtyfive chapters. There is not any mention either in these first chapters to conditional operations such as purchases or barters made on the condition of receiving the merchandise in good state, of which an example is provided in the second and last section, unnumbered, included in the appendix under the title “Casi che acade mettere ale recordange del mercante,” i.e., “Cases that must be recorded in the merchant’s Agenda.

On the other hand, and from a formal point of view, perhaps it should also be added that, in the first unnumbered section, the full stop is used much more than in the previous text.
Even disregarding the ten examples of ledger entries at the end of the Treatise (Tuscan vs. Venetian style) and the differences between Chapter 36 (and the following unnumbered sections) and the first part of Luca Pacioli’s accounting treatise, one other such difference must be added. While in these last parts Pacioli uses correctly the word “conto” for “account” and the word “partita” for “entry,” in the former thirtyfive chaptes, he uses the expression “partita” indistinctly to designate an account or an entry, as we have already mentioned.

Likewise, it must also be stated that the denomination “quaderno” is never used in the appendix to designate the Ledger, as it was habitually used in the previous chapters. Instead, Pacioli uses the expression “libro de mercanti” or, simply, “libro,” words that were also used in several occasions in the former chapters.

In view of all the above, there seems to be indeed good reasons to believe that Chapter 36 of the Treatise is not really a summary of the first thirtyfive chapters, as Pacioli says, but that it is a separate, though certainly very condensed, text that was not meant to be a summary of the preceding chapters but was written for a different purpose. In the same way, it can also be said that neither the ten related Ledger entries provided at the end of the Treatise, nor the two unnumbered sections after Chapter 36 seem to have been written originally for the purpose of being a part of the Treatise. This is the case irrespective of whether all these sections are considered as a unit per se together with Chapter 36 or, on the contrary, as separate elements.

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